There was another Universe before ours, and the one we live in is flat. These two discoveries in 2010 revolutionized man's understanding of the evolution of the cosmos. Scientists have proven that 70 percent of the mass of the Universe consists of a mysterious “dark energy” that accelerates its expansion. If both theories are confirmed, this could be a new step in understanding the world.
The first discovery was made by one of the most brilliant physicists of our time - Roger Penrose of Oxford University. He wondered: what preceded the Big Bang, as a result of which, according to the dominant theory, time, matter and space were formed?
As a result of his research, Penrose discovered evidence of the existence of another universe that preceded ours. And in general, according to the scientist, the development of the universe occurs cyclically: universes are born, die and are born again from their own ashes, living through periods that the physicist called “eons.” His theory helps explain why the Universe was originally very orderly, allowing very complex objects to form.
The second study, published in Nature, was carried out by Christian Marinoni and Edline Buzzi, French physicists at the University of Provence. It takes us back to Albert Einstein's long-forgotten theory that our Universe is flat. At one time, Einstein abandoned it, considering it erroneous. However, it is precisely this form of the Universe that makes it possible to explain the existence of “dark energy” - the main driving force of the Universe. French researchers have proven that 74 percent of the mass of the Universe consists of this energy, which accelerates its expansion.
Today the dominant theory is that the Universe arose 13.7 billion years ago from a single point large
density, which as a result of the Big Bang in the first moments of existence was a “hot soup” of free particles not bound into atoms. The temperature of this “soup” was thousands of millions of degrees (these conditions were recently successfully reproduced in the Large Hadron Collider - LHC). Having been born, the Universe began to rapidly expand and cool, particles began to form the first simplest atoms (hydrogen), and gravitational forces worked for a long time to combine atoms into the matter of stars and galaxies.
One of the most pressing questions is the question of why, after the Big Bang, the rate of expansion of the Universe not only did not slow down, but increased? As a result, scientists came to the conclusion that this largely depends on the mass of the substance contained in it. If the total mass of matter in the Universe is sufficient for the force of gravity (which is stronger the greater the mass) to overcome the primary centrifugal force of the Big Bang, then the expansion of the Universe will be stopped and may even lead to its collapse - a collapse that scientists call the Big Crunch. However, if the total mass is insufficient, nothing will be able to stop the expansion of the Universe, it will tend to become a large black void where the last star will eventually go out.
It remains to measure the mass of the Universe, but science has encountered many surprises here. The first is that the ordinary matter that makes up galaxies, stars and planets, and which exists as light and other measurable radiation, makes up only 5 percent of the total mass of the Universe, which is absolutely not enough to slow down its run-up. The other 25 percent corresponds to another "type of matter" that cannot be directly detected by our instruments because it emits nothing. This matter is known as "dark". We know where it is (called "black holes") because we can measure changes in gravity, but no one has ever been able to "see" it. One can only speculate about what particles it might consist of.
Indeed, what properties should these particles have? It is absolutely obvious that they should not decay into other, lighter ones, otherwise they would have had to decay long ago during the entire existence of the Universe. This fact itself indicates that a new, not yet discovered conservation law operates in nature, prohibiting these particles from decaying. The analogy here is with the law of conservation of electric charge: an electron is the lightest particle with an electric charge, and that is why it does not decay into lighter particles (for example, neutrinos and photons).
Further, dark matter particles interact extremely weakly with our matter, otherwise they would have already been discovered in earthly experiments. As a matter of fact, this is where scientists’ knowledge about these interesting particles ends and an open field of guesses and assumptions begins.
So, with dark matter, which makes up that same 25 percent, at least something is clear. But what is the other 70 percent? Scientists are not yet able to give a definite answer to this question and use the term “dark energy”. However, even less is known about it than about dark matter.
The most unusual thing about all this is that dark energy, in a sense, experiences anti-gravity. It is thanks to this that the expansion of the Universe does not slow down, but accelerates. This picture, generally speaking, does not contradict the general theory of relativity, but for this, dark energy must have a special property - negative pressure. This sharply distinguishes it from ordinary forms of matter. It would not be an exaggeration to say that the nature of dark energy is the main mystery of fundamental physics of the 21st century. Although there is already one candidate for this role - the usual, well-known vacuum. True, its nature also still remains very mysterious.
It is this force that presumably determines the increase in the speed of the Universe. It was this dark energy that Penrose and scientists from France explored. Penrose analyzed data obtained from the WMAP satellite (which measured the microwave radiation that permeates the entire Universe and is a trace of the Big Bang). He discovered distribution patterns in the form of concentric circles, which can be explained as traces of the existence of other universes (superposition of old radiation on new). This means that our Universe is one in a series of many, and the time will come when it will die and be reborn as a result of a new Big Bang. Before "death" the Universe will become "smooth and linear."
This conclusion is confirmed by Buzzi and Marinoni, who proved by measuring the distortions of light coming from 500 pairs of galaxies that we live in a flat universe, and not a curved or spherical one, as many thought. Starting from the postulate that geometric measurements can be used to determine the composition of the Universe, scientists studied the distribution of the relative orientation of pairs of galaxies orbiting each other. In a Universe without dark energy, this distribution would be spherically symmetric, that is, the number of pairs oriented in any direction would be the same.
Observations showed that, in fact, the farther galaxy pairs were from Earth, the more asymmetrical the distribution of their orientation was - more pairs were located along the line of sight from Earth. In addition, if the Universe were spherical or curved, then we would see the image of galaxies deformed, as if we were looking into a metal ball and seeing our face distorted there. There are no distortions in flat space, which was noted.
What is dark matter or hidden mass? What about dark energy?
Hidden mass (in cosmology and astrophysics also dark matter, dark matter) is the general name for a set of astronomical objects that are inaccessible to direct observations by modern means of astronomy (that is, not emitting electromagnetic or neutrino radiation of sufficient intensity for observations), but observable indirectly by the gravitational effects exerted by to visible objects.
The general hidden mass problem consists of two problems:
* astrophysical, that is, the contradiction of the observed mass of gravitationally bound objects and their systems, such as galaxies and their clusters, with their observed parameters determined by gravitational effects;
* cosmological - contradictions between the observed cosmological parameters and the average density of the Universe obtained from astrophysical data.
Nature and composition of latent mass
In addition to direct observations of the gravitational effects of hidden mass, there are a number of objects that are difficult to observe directly, but which may contribute to the composition of the hidden mass. Currently, objects of baryonic and non-baryonic nature are being considered: if the former include fairly well-known astronomical objects, then neutrinos, strapelles and hypothetical elementary particles following from classical quantum chromodynamics (axions) and supersymmetric extensions of quantum field theories are considered as candidates for the latter.
To explain the deviation of the rotation velocities of galactic objects from Keplerian ones, the presence of a massive dark halo of galaxies should be assumed. Massive objects in the halo of galaxies include weakly emitting compact objects, primarily low-mass stars - brown dwarfs, substars or very massive Jupiter-like planets, the mass of which is insufficient to initiate thermonuclear reactions in their cores, cooled white dwarfs, neutron stars and black holes.
What is this?
What do we know today about dark matter, which makes up 95% of the mass of the Universe? Almost nothing. But we still know something. First of all, there is no doubt that dark matter exists - this is irrefutably evidenced by the facts given above. We also know for certain that dark matter exists in several forms. After, by the beginning of the 21st century, as a result of many years of observations in the SuperKamiokande (Japan) and SNO (Canada) experiments, it was established that neutrinos have mass, it became clear that from 0.3% to 3% of the 95% of the hidden mass lies in neutrinos, which have long been familiar to us - even if their mass is extremely small, but the number in the Universe is approximately a billion times greater than the number of nucleons: each cubic centimeter contains on average 300 neutrinos. The remaining 92–95% consists of two parts - dark matter and dark energy. A small fraction of dark matter is ordinary baryonic matter, built from nucleons; the remainder is apparently accounted for by some unknown massive weakly interacting particles (the so-called cold dark matter).
Baryonic dark matter
A small (4–5%) portion of dark matter is ordinary matter that emits little or no radiation of its own and is therefore invisible. The existence of several classes of such objects can be considered experimentally confirmed. The most complex experiments, based on the same gravitational lensing, led to the discovery of so-called massive compact halo objects, that is, located on the periphery of galactic disks. This required monitoring millions of distant galaxies over several years. When a dark, massive body passes between an observer and a distant galaxy, its brightness briefly decreases (or increases as the dark body acts as a gravitational lens). As a result of painstaking searches, such events were identified. The nature of massive compact halo objects is not completely clear. Most likely, these are either cooled stars (brown dwarfs) or planet-like objects that are not associated with stars and travel around the galaxy on their own. Another representative of baryonic dark matter is hot gas recently discovered in galaxy clusters using X-ray astronomy methods, which does not glow in the visible range.
Nonbaryonic dark matter
The main candidates for nonbaryonic dark matter are the so-called WIMPs (short for Weakly Interactive Massive Particles). The peculiarity of WIMPs is that they show almost no interaction with ordinary matter. This is why they are the real invisible dark matter, and why they are extremely difficult to detect. The mass of WIMP must be at least tens of times greater than the mass of a proton. The search for WIMPs has been carried out in many experiments over the past 20–30 years, but despite all efforts, they have not yet been detected
One idea is that if such particles exist, then the Earth, as it orbits the Sun with the Sun around the galactic center, should be flying through a rain of WIMPs. Despite the fact that WIMP is an extremely weakly interacting particle, it still has a very small probability of interacting with an ordinary atom. At the same time, in special installations - very complex and expensive - a signal can be recorded. The number of such signals should change throughout the year because, as the Earth moves in orbit around the Sun, it changes its speed and direction relative to the wind, which consists of WIMPs. The DAMA experimental group, working at Italy's Gran Sasso underground laboratory, reports observed year-to-year variations in signal count rates. However, other groups have not yet confirmed these results, and the question essentially remains open.
Another method of searching for WIMPs is based on the assumption that during billions of years of their existence, various astronomical objects (Earth, Sun, the center of our Galaxy) should capture WIMPs, which accumulate in the center of these objects, and, annihilating each other, give rise to a neutrino stream . Attempts to detect excess neutrino flux from the center of the Earth towards the Sun and the center of the Galaxy were made on underground and underwater neutrino detectors MACRO, LVD (Gran Sasso Laboratory), NT-200 (Lake Baikal, Russia), SuperKamiokande, AMANDA (Scott Station -Amundsen, South Pole), but have not yet led to a positive result.
Experiments to search for WIMPs are also actively carried out at particle accelerators. According to Einstein's famous equation E=mc2, energy is equivalent to mass. Therefore, by accelerating a particle (for example, a proton) to a very high energy and colliding it with another particle, one can expect the creation of pairs of other particles and antiparticles (including WIMPs), the total mass of which is equal to the total energy of the colliding particles. But accelerator experiments have not yet led to a positive result.
Dark energy
Even less can be said about dark energy than about dark matter. First, it is evenly distributed throughout the Universe, unlike ordinary matter and other forms of dark matter. There is as much of it in galaxies and galaxy clusters as outside of them. Secondly, it has several very strange properties, which can only be understood by analyzing the equations of the theory of relativity and interpreting their solutions. For example, dark energy experiences antigravity: due to its presence, the rate of expansion of the Universe increases. Dark energy seems to push itself away, accelerating the scattering of ordinary matter collected in galaxies. Dark energy also has negative pressure, due to which a force arises in the substance that prevents it from stretching.
The main candidate for the role of dark energy is vacuum. The vacuum energy density does not change as the Universe expands, which corresponds to negative pressure. Another candidate is a hypothetical super-weak field, called quintessence. Hopes for clarifying the nature of dark energy are associated primarily with new astronomical observations. Progress in this direction will undoubtedly bring radically new knowledge to humanity, since in any case, dark energy must be a completely unusual substance, completely different from what physics has dealt with so far.
So, 95% of our world consists of something about which we know almost nothing. One can have different attitudes towards such a fact that is beyond any doubt. It can cause anxiety, which always accompanies a meeting with something unknown. Or disappointment, because such a long and complex path to constructing a physical theory that describes the properties of our world led to the statement: most of the Universe is hidden from us and unknown to us.
Doctor of Physical and Mathematical Sciences A. MADERA.
What do a piece of paper, a table surface, a donut and a mug have in common?
Two-dimensional analogues of Euclidean, spherical and hyperbolic geometries.
A Möbius strip with a point a on its surface, a normal to it and a small circle with a given direction v.
A flat sheet of paper can be glued into a cylinder and, by connecting its ends, you can get a torus.
A torus with one handle is homeomorphic to a sphere with two handles - their topology is the same.
If you cut out this figure and glue a cube out of it, it will become clear what a three-dimensional torus looks like, endlessly repeating copies of the green “worm” sitting in its center.
A three-dimensional torus can be glued together from a cube, just as a two-dimensional torus can be glued together from a square. Multi-colored “worms” traveling inside it clearly demonstrate which faces of the cube are glued together.
The cube, the fundamental region of a three-dimensional torus, is cut into thin vertical layers that, when glued together, form a ring of two-dimensional tori.
If two faces of the original cube are glued together with a 180-degree rotation, a 1/2-rotated cubic space is formed.
Rotating two faces 90 degrees gives a 1/4-rotated cubic space. Try these drawings and similar drawings on page 88 as inverted stereo pairs. “Worms” on non-rotated edges will gain volume.
If we take a hexagonal prism as a fundamental area, glue each of its faces directly to the opposite one, and rotate the hexagonal ends by 120 degrees, we get a 1/3-rotated hexagonal prismatic space.
Rotating the hexagonal face 60 degrees before gluing produces a 1/6-rotated hexagonal prismatic space.
Double cubic space.
Plate space occurs when the top and bottom sides of an infinite plate are glued together.
Tubular spaces - straight (A) and rotated (B), in which one of the surfaces is glued to the opposite one with a rotation of 180 degrees.
The distribution map of the microwave background radiation shows the distribution of matter density that was 300 thousand years ago (shown in color). Its analysis will make it possible to determine what topology the Universe has.
In ancient times, people believed that they lived on a vast flat surface, although covered here and there with mountains and depressions. This belief persisted for many thousands of years until Aristotle in the 4th century BC. e. I didn’t notice that a ship going out to sea disappears from sight not because as it moves away it shrinks to dimensions inaccessible to the eye. On the contrary, first the hull of the ship disappears, then the sails and, finally, the masts. This led him to the conclusion that the Earth must be round.
Over the past millennia, many discoveries have been made and enormous experience has been accumulated. And yet, fundamental questions still remain unanswered: is the Universe in which we live finite or infinite, and what is its shape?
Recent observations by astronomers and research by mathematicians show that the shape of our Universe should be sought among eighteen so-called three-dimensional orientable Euclidean manifolds, and only ten can lay claim to it.
OBSERVABLE UNIVERSEAny conclusions about the possible shape of our Universe must be based on real facts obtained from astronomical observations. Without this, even the most beautiful and plausible hypotheses are doomed to failure. Therefore, let's see what the observational results say about the Universe.
First of all, we note that, no matter where we are in the Universe, around any point we can outline a sphere of arbitrary size containing the space of the Universe inside. This somewhat artificial construction tells cosmologists that the space of the Universe is a three-dimensional manifold (3-manifold).
The question immediately arises: what kind of diversity represents our Universe? Mathematicians have long established that there are so many of them that a complete list still does not exist. Long-term observations have shown that the Universe has a number of physical properties that sharply reduce the number of possible candidates for its shape. And one of the main properties of the topology of the Universe is its curvature.
According to the concept accepted today, approximately 300 thousand years after the Big Bang, the temperature of the Universe dropped to a level sufficient for electrons and protons to combine into the first atoms (see “Science and Life” Nos. 11, 12, 1996). When this happened, radiation that had initially been scattered by charged particles was suddenly able to pass unhindered through the expanding Universe. This radiation, now known as the cosmic microwave background, or relict radiation, is surprisingly uniform and reveals only very weak deviations (fluctuations) of intensity from the average value (see Science and Life No. 12, 1993). Such homogeneity can only exist in the Universe, the curvature of which is constant everywhere.
The constancy of curvature means that the space of the Universe has one of three possible geometries: flat Euclidean spherical with positive curvature or hyperbolic with negative. These geometries have completely different properties. For example, in Euclidean geometry, the sum of the angles of a triangle is exactly 180 degrees. This is not the case in spherical and hyperbolic geometries. If you take three points on a sphere and draw straight lines between them, then the sum of the angles between them will be more than 180 degrees (up to 360). In hyperbolic geometry, this sum is less than 180 degrees. There are other fundamental differences.
So which geometry should we choose for our Universe: Euclidean, spherical or hyperbolic?
The German mathematician Carl Friedrich Gauss understood in the first half of the 19th century that the real space of the surrounding world could be non-Euclidean. Carrying out many years of geodetic work in the Kingdom of Hanover, Gauss set out to explore the geometric properties of physical space using direct measurements. To do this, he chose three mountain peaks distant from one another - Hohenhagen, Inselberg and Brocken. Standing on one of these peaks, he directed the sun's rays reflected by the mirrors onto the other two and measured the angles between the sides of a huge triangle of light. Thus, he tried to answer the question: are the trajectories of light rays passing over the spherical space of the Earth bent? (By the way, around the same time, the Russian mathematician, rector of Kazan University Nikolai Ivanovich Lobachevsky proposed to experimentally study the question of the geometry of physical space using a star triangle.) If Gauss had discovered that the sum of the angles of the light triangle differs from 180 degrees, then the conclusion would have followed that the sides of the triangle are curved and real physical space is non-Euclidean. However, within the limits of measurement error, the sum of the angles of the “Brocken - Hohenhagen - Inselberg test triangle” was exactly 180 degrees.
So, on a small (by astronomical standards) scale, the Universe appears as Euclidean (although, of course, it is impossible to extrapolate Gauss’s conclusions to the entire Universe).
Recent studies using high-altitude balloons flown over Antarctica also support this conclusion. When measuring the angular power spectrum of the CMB, a peak was detected, which the researchers believe can only be explained by the existence of cold black matter - relatively large, slowly moving objects - precisely in the Euclidean Universe. Other studies also support this conclusion, which sharply reduces the number of likely candidates for the possible shape of the Universe.
Back in the thirties of the 20th century, mathematicians proved that there are only 18 different Euclidean three-dimensional manifolds and, therefore, only 18 possible forms of the Universe instead of an infinite number. Understanding the properties of these manifolds helps to experimentally determine the true shape of the Universe, since a targeted search is always more effective than a blind search.
However, the number of possible forms of the Universe can be further reduced. Indeed, among the 18 Euclidean 3-manifolds, there are 10 orientable and 8 non-orientable. Let us explain what the concept of orientability is. To do this, consider an interesting two-dimensional surface - the Möbius strip. It can be obtained from a rectangular strip of paper, twisted once and glued at the ends. Now let’s take a point on the Möbius strip A, draw a normal (perpendicular) to it, and around the normal we draw a small circle with a counterclockwise direction when viewed from the end of the normal. Let's start moving the point along with the normal and the directed circle along the Möbius strip. When the point goes around the entire sheet and returns to its original position (visually it will be on the other side of the sheet, but in geometry the surface has no thickness), the direction of the normal will change to the opposite, and the direction of the circle will change to the opposite. Such trajectories are called orientation-reversing paths. And surfaces that have them are called non-orientable or one-sided. Surfaces on which there are no closed paths reversing the orientation, for example, a sphere, a torus and an untwisted ribbon, are called orientable or two-sided. Note by the way that the Möbius strip is a Euclidean non-orientable two-dimensional manifold.
If we assume that our Universe is a non-orientable manifold, then physically this would mean the following. If we fly from the Earth along a closed loop that reverses the orientation, then, of course, we will return home, but we will find ourselves in a mirror copy of the Earth. We will not notice any changes in ourselves, but in relation to us, the rest of the inhabitants of the Earth will have a heart on the right, all the clocks will go counterclockwise, and the texts will appear in a mirror image.
It is unlikely that we live in such a world. Cosmologists believe that if our Universe were non-orientable, then energy would be emitted from the boundary zones in which matter and antimatter interact. However, nothing like this has ever been observed, although theoretically it can be assumed that such zones exist outside the region of the Universe accessible to our view. Therefore, it is reasonable to exclude eight non-orientable manifolds from consideration and limit the possible forms of our Universe to ten orientable Euclidean three-dimensional manifolds.
POSSIBLE FORMS OF THE UNIVERSEThree-dimensional manifolds in four-dimensional space are extremely difficult to visualize. However, we can try to imagine their structure if we apply the approach used in topology to visualize two-dimensional manifolds (2-manifolds) in our three-dimensional space. All objects in it are considered to be made of some kind of durable elastic material like rubber, allowing any stretching and curvature, but without tears, folds and gluing. In topology, figures that can be transformed from one to another using such deformations are called homeomorphic; they have the same internal geometry. Therefore, from a topological point of view, a donut (torus) and an ordinary cup with a handle are one and the same. But it is impossible to transform a soccer ball into a donut. These surfaces are topologically different, that is, they have different internal geometric properties. However, if you cut a round hole on a sphere and attach one handle to it, then the resulting figure will already be homeomorphic to a torus.
There are many surfaces that are topologically distinct from the torus and the sphere. For example, by adding a handle to the torus, similar to the one we see on the cup, we get a new hole, and therefore a new figure. A torus with a handle will be homeomorphic to a pretzel-shaped figure, which in turn is homeomorphic to a sphere with two handles. The addition of each new handle creates another hole and therefore a different surface. In this way you can get an infinite number of them.
All such surfaces are called two-dimensional manifolds or simply 2-manifolds. This means that a circle of arbitrary radius can be drawn around any point. On the surface of the Earth you can draw a circle containing its points. If we see only such a picture, it is reasonable to assume that it represents an infinite plane, a sphere, a torus, or indeed any other surface from an infinite number of tori or spheres with a varying number of handles.
These topological shapes can be quite difficult to understand. And in order to imagine them easier and more clearly, let’s glue a cylinder from a square sheet of paper, connecting its left and right sides. The square in this case is called the fundamental area for the torus. If you now mentally glue the bases of the cylinder together (the material of the cylinder is elastic), you will get a torus.
Let's imagine that there is some two-dimensional creature, say an insect, whose movement along the surface of the torus needs to be studied. This is not easy to do, and it is much more convenient to observe its movement in a square - a space with the same topology. This technique has two advantages. Firstly, it allows you to clearly see the path of an insect in three-dimensional space, following its movement in two-dimensional space, and secondly, it allows you to remain within the framework of well-developed Euclidean geometry on a plane. Euclidean geometry contains a postulate about parallel lines: for any straight line and a point outside it, there is a unique straight line parallel to the first and passing through this point. In addition, the sum of the angles of a plane triangle is exactly 180 degrees. But since the square is described by Euclidean geometry, we can extend it to the torus and claim that the torus is a Euclidean 2-manifold.
The indistinguishability of internal geometries for a variety of surfaces is associated with their important topological characteristic, called developability. Thus, the surfaces of a cylinder and a cone look completely different, but nevertheless their geometries are absolutely the same. Both of them can be deployed in a plane without changing the lengths of the segments and angles between them, therefore Euclidean geometry is valid for them. The same applies to the torus, since it is a surface that develops into a square. Such surfaces are called isometric.
Countless numbers of tori can be formed from other flat figures, for example from various parallelograms or hexagons, by gluing their opposite edges. However, not every quadrilateral is suitable for this: the lengths of its glued sides must be the same. This requirement is necessary to avoid, when gluing, extensions or compressions of the edges of the area, which violate the Euclidean geometry of the surface.
Now let's move on to varieties of higher dimensions.
REPRESENTATION OF POSSIBLE FORMS OF THE UNIVERSELet's try to imagine the possible forms of our Universe, which, as we have already seen, must be sought among ten orientable Euclidean three-dimensional manifolds.
To represent a Euclidean 3-manifold, we apply the method used above for two-dimensional manifolds. There we used a square as the fundamental region of the torus, and to represent a three-dimensional manifold we will take three-dimensional objects.
Let's take a cube instead of a square and, just as we glued the opposite edges of the square, glue together the opposite faces of the cube at all their points.
The resulting three-dimensional torus is a Euclidean 3-manifold. If we somehow ended up in it and looked forward, we would see the back of our heads, as well as copies of ourselves in each face of the cube - in front, behind, left, right, above and below. Behind them we would see an infinite number of other copies, just as if we were in a room where the walls, floor and ceiling are covered with mirrors. But the images in a three-dimensional torus will be straight, not mirrored.
It is important to note the circular nature of this and many other manifolds. If the Universe really had this shape, then if we left Earth and flew without any change in course, we would eventually return home. Something similar is observed on Earth: moving west along the equator, we will sooner or later return to our starting point from the east.
By cutting the cube into thin vertical layers, we get a set of squares. The opposite edges of these squares must be glued together because they make up the opposite faces of the cube. So the three-dimensional torus turns out to be a ring consisting of two-dimensional tori. Recall that the front and back squares are also glued together and serve as the faces of the cube. Topologists denote such a manifold as T 2 xS 1 , where T 2 means a two-dimensional torus and S 1 means a ring. This is an example of a bundle, or bundle, of tori.
Three-dimensional tori can be obtained not only using a cube. Just as a parallelogram forms a 2-torus, by gluing together opposite faces of a parallelepiped (a three-dimensional body bounded by parallelograms), we will create a 3-torus. From different parallelepipeds spaces are formed with different closed paths and angles between them.
These and all other finite manifolds are very simply included in the picture of the expanding Universe. If the fundamental area of diversity is constantly expanding, the space formed by it will also expand. Each point in expanding space moves further and further away from the others, which exactly corresponds to the cosmological model. However, it must be taken into account that points near one face will always be adjacent to points on the opposite face, since, regardless of the size of the fundamental region, the opposite faces are glued together.
The next three-dimensional manifold, similar to a three-dimensional torus, is called 1/2 - rotated cubic space. In this space, the fundamental area is again the cube or parallelepiped. Four edges are glued as usual, and the remaining two, front and back, are glued with a 180-degree rotation: the top of the front edge is glued to the bottom of the back. If we found ourselves in such diversity and looked at one of these faces, we would see our own copy, but turned upside down, followed by an ordinary copy, and so on ad infinitum. Like a three-dimensional torus, the fundamental region of a 1/2-rotated cubic space can be sliced into thin vertical layers so that when glued together, the result is again a bundle of two-dimensional tori, except this time the front and back tori are glued together with a 180-degree rotation .
A 1/4-rotated cubic space is the same as the previous one, but rotated 90 degrees. However, since the rotation is only a quarter, it cannot be obtained from any parallelepiped - its front and back parts must be squares to avoid curvature and skew of the fundamental area. In the front face of the cube, we would see another one behind our copy, rotated 90 degrees relative to it.
A 1/3-rotated hexagonal prismatic space uses a hexagonal prism rather than a cube as its fundamental region. To obtain it, you need to glue each face, which is a parallelogram, with its opposite face, and two hexagonal faces with a rotation of 120 degrees. Each hexagonal layer of this manifold is a torus, and thus the space is also a bundle of tori. In all hexagonal faces we would see copies rotated 120 degrees relative to the previous one, and copies in parallelogram faces are straight.
The 1/6-rotated hexagonal prismatic space is constructed similarly to the previous one, but with the difference that the front hexagonal face is glued to the back with a 60-degree rotation. As before, in the resulting bundle of tori the remaining faces - parallelograms - are glued directly to one another.
Double cubic space is radically different from previous manifolds. This finite space is no longer a bundle of tori and has an unusual gluing structure. Double cube space, however, uses a simple fundamental area, which is two cubes stacked on top of each other. When gluing, not all faces are directly connected: the top front and back faces are glued to the faces directly below them. In this space, we would see ourselves in a kind of perspective - the soles of our feet would be right in front of our eyes.
This concludes the list of finite orientable Euclidean three-dimensional, so-called compact manifolds. It is likely that among them we need to look for the shape of our Universe.
Many cosmologists believe that the Universe is finite: it is difficult to imagine the physical mechanism for the emergence of an infinite Universe. Nevertheless, we will consider the four remaining orientable non-compact Euclidean three-dimensional manifolds until real data are obtained that exclude their existence.
The first and simplest infinite three-dimensional manifold is Euclidean space, which is studied in high school (it is denoted R 3). In this space, the three axes of Cartesian coordinates extend to infinity. In it we do not see any copies of ourselves, neither straight, nor rotated, nor inverted.
The next manifold is the so-called plate space, the fundamental region of which is an infinite plate. The upper part of the plate, which is an infinite plane, is glued directly to its lower part, also an infinite plane. These planes must be parallel to one another, but can be arbitrarily shifted when gluing, which is unimportant, given their infinity. In topology, this manifold is written as R 2 xS 1, where R 2 denotes a plane and S 1 a ring.
The last two 3-manifolds use infinitely long tubes as fundamental domains. The tubes have four sides, their cross-sections are parallelograms, they have neither top nor bottom - their four sides extend indefinitely. As before, the nature of the gluing of the fundamental domain determines the shape of the manifold.
The tubular space is formed by gluing together both pairs of opposite sides. After gluing, the original parallelogram-shaped section becomes a two-dimensional torus. In topology, this space is written as the product T 2 xR 1.
By rotating one of the bonded surfaces of the tubular space by 180 degrees, we obtain a rotated tubular space. This rotation, taking into account the infinite length of the tube, gives it unusual characteristics. For example, two points located very far from one another, at different ends of the fundamental region, after gluing will be nearby.
What is the shape of our Universe after all?
In order to choose one of the above ten Euclidean 3-manifolds as the form of our Universe, additional data from astronomical observations is needed.
The easiest way would be to find copies of our Galaxy in the night sky. Having discovered them, we will be able to establish the nature of the gluing of the fundamental region of the Universe. If it turns out that the Universe is a 1/4-rotated cubic space, then straight copies of our Galaxy will be visible from four sides, and rotated 90 degrees from the remaining two. However, despite its apparent simplicity, this method is of little use for establishing the shape of the Universe.
Light travels at a finite speed, so when we observe the Universe, we are essentially looking into the past. Even if we one day discover an image of our Galaxy, we will not be able to recognize it, because in its “young years” it looked completely different. It is too difficult to recognize a copy of ours from the huge number of galaxies.
At the beginning of the article it was said that the Universe has constant curvature. The homogeneity of the cosmic microwave background radiation directly indicates this. However, it has slight spatial variations of about 10 -5 kelvin, indicating that there were minor fluctuations in the density of matter in the early Universe. As the expanding Universe cooled, the matter in these regions eventually created galaxies, stars and planets. The map of microwave radiation allows you to look into the past, to the times of initial irregularities, to see the outlines of the Universe, which was then a thousand times smaller. To appreciate the meaning of this map, consider a hypothetical example: the Universe in the form of a two-dimensional torus.
In the three-dimensional Universe, we observe the sky in all directions, that is, within a sphere. Two-dimensional inhabitants of a two-dimensional Universe would be able to observe it only within a circle. If this circle were smaller than the fundamental region of their Universe, they could get no indication of its shape. If, however, the circle of vision of two-dimensional creatures is larger than the fundamental region, they would be able to see intersections and even repetitions of patterns in the Universe and try to find points with the same temperatures that correspond to the same region. If there were enough such points in their vision circle, they could conclude that they live in a torus Universe.
Even though we live in a three-dimensional universe and see a spherical region, we face the same problem as two-dimensional creatures. If our sphere of vision is smaller than the fundamental region of the Universe 300,000 years ago, we will not see anything unusual. Otherwise, the sphere will intersect it in circles. By finding two circles that have the same variations in microwave radiation, cosmologists can compare their orientations. If the circles are arranged crosswise, this will mean there is gluing, but without rotation. Some of them, however, can be combined according to a quarter or half turn. If enough of these circles can be discovered, the mystery of the fundamental region of the Universe and its gluing together will be revealed.
However, until an accurate map of microwave radiation appears, cosmologists will not be able to draw any conclusions. In 1989, researchers from NASA attempted to create a map of the cosmic microwave background radiation. However, the angular resolution of the satellite was about 10 degrees, which did not allow accurate measurements to be made that would satisfy cosmologists. In the spring of 2002, NASA made a second attempt and launched a probe that mapped temperature fluctuations with an angular resolution of about 0.2 degrees. In 2007, the European Space Agency plans to use the Planck satellite, which has an angular resolution of 5 arc seconds.
If the launches are successful, then within four to ten years accurate maps of CMB fluctuations will be obtained. And if the size of the sphere of our vision turns out to be large enough, and the measurements are sufficiently accurate and reliable, we will finally know what shape our Universe has.
Based on materials from the magazines "American Scientist" and "Popular Science".When astronomers and physicists say that the Universe is flat, they do not mean that the Universe is flat as a sheet. We are talking about the property of three-dimensional flatness - Euclidean (uncurved) geometry in three dimensions. In Euclidean astronomy, the world is a convenient comparative model of the surrounding space. Matter in such a world is distributed homogeneously, that is, a unit volume contains the same amount of matter, and isotropic, that is, the distribution of matter is the same in all directions. In addition, matter does not evolve there (for example, radio sources do not light up and supernovae do not erupt), and space is described by the simplest geometry. This is a very convenient world to describe, but not to live in, since there is no evolution there.
It is clear that such a model does not correspond to observational facts. The matter around us is distributed inhomogeneously and anisotropically (somewhere there are stars and galaxies, and somewhere there are none), accumulations of matter evolve (change over time), and space, as we know from the experimentally confirmed theory of relativity, is curved.
What is curvature in three-dimensional space? In the Euclidean world, the sum of the angles of any triangle is 180 degrees - in all directions and in any volume. In non-Euclidean geometry - in curved space - the sum of the angles of a triangle will depend on the curvature. Two classic examples are a triangle on a sphere, where the curvature is positive, and a triangle on a saddle-shaped surface, where the curvature is negative. In the first case, the sum of the angles of the triangle is greater than 180 degrees, and in the second case, it is less. When we typically talk about a sphere or a saddle, we think of curved two-dimensional surfaces surrounding three-dimensional bodies. When we talk about the Universe, we must understand that we are moving to the concept of three-dimensional curved space - for example, we are no longer talking about a two-dimensional spherical surface, but about a three-dimensional hypersphere.
So why is the Universe flat in a three-dimensional sense, if space is curved not only by clusters of galaxies, our Galaxy and the Sun, but even by the Earth? In cosmology, the Universe is considered as a whole object. And as a whole object it has certain properties. For example, starting from some very large linear scales (here we can consider 60 megaparsecs [~180 million light years] and 150 Mpc), matter in the Universe is distributed uniformly and isotropically. On smaller scales, clusters and superclusters of galaxies and voids between them are observed - voids, that is, the homogeneity is broken.
How can we measure the flatness of the Universe as a whole if information about the distribution of matter in clusters is limited by the sensitivity of our telescopes? It is necessary to observe other objects in a different range. The best thing that nature has given us is the cosmic microwave background, or , which, having separated from matter 380 thousand years after the Big Bang, contains information about the distribution of this matter literally from the first moments of the existence of the Universe.
The curvature of the Universe is associated with a critical density equal to 3H 2 /8πG (where H is the Hubble constant, G is the gravitational constant), which determines its shape. The value of the parameter is very small - about 9.3 × 10 -27 kg/m 3, or 5.5 hydrogen atoms per cubic meter. This parameter distinguishes the simplest cosmological models built on Friedmann’s equations, which describe: if the density is higher than critical, then space has a positive curvature and the expansion of the Universe in the future will be replaced by compression; if below critical, then space has negative curvature and the expansion will be eternal; if the critical density is equal, the expansion will also be eternal with a transition in the distant future to the Euclidean world.
Cosmological parameters that describe the density of the Universe (and the main ones are the density of dark energy, the density of dark matter and the density of baryonic [visible] matter) are expressed as a ratio to the critical density. According to , obtained from measurements of cosmic microwave background radiation, the relative density of dark energy is Ω Λ = 0.6879 ± 0.0087, and the relative density of all matter (that is, the sum of the densities of dark and visible matter) is Ω m = 0.3121 ± 0.0087.
If we add up all the energy components of the Universe (densities of dark energy, all matter, as well as less significant densities of radiation and neutrinos in our era, and others), then we obtain the density of all energy, which is expressed through the ratio to the critical density of the Universe and denoted Ω 0. If this relative density is 1, then the curvature of the Universe is 0. The deviation Ω 0 from unity describes the energy density of the Universe Ω K associated with the curvature. By measuring the level of inhomogeneities (fluctuations) in the distribution of the relict background radiation, all density parameters, their total value and, as a consequence, the curvature parameter of the Universe are determined.
Based on the observational results, taking into account only the CMB data (temperature, polarization and lensing), it was determined that the curvature parameter is very close to zero within small errors: Ω K = -0.004±0.015, - and taking into account data on the distribution of galaxy clusters and measurements expansion rate according to data on type Ia supernovae, the parameter Ω K = 0.0008±0.0040. That is, the Universe is flat with high accuracy.
Why is it important? The flatness of the Universe is one of the main indicators of the era of very fast, described by the inflationary model. For example, at the moment of birth the Universe could have had a very large curvature, while now, according to CMB data, it is known that it is flat. Inflationary expansion makes it flat throughout observable space (meaning, of course, large scales on which the curvature of space by stars and galaxies is not significant) just as an increase in the radius of a circle straightens the latter, and with an infinite radius the circle looks like a straight line.
In ancient times, people thought that the earth was flat and stood on three whales, then it turned out that our ecumene is round and if you sail all the time to the west, then after a while you will return to your starting point from the east. Views of the Universe changed in a similar way. At one time, Newton believed that space was flat and infinite. Einstein allowed our World to be not only limitless and crooked, but also closed. The latest data obtained during the study of cosmic microwave background radiation indicate that the Universe may well be closed on itself. It turns out that if you fly away from the earth all the time, then at some point you will begin to approach it and eventually return back, going around the entire Universe and traveling around the world, just as one of Magellan’s ships, having circled the entire globe, sailed to the Spanish port of Sanlúcar de Barrameda.
The hypothesis that our Universe was born as a result of the Big Bang is now considered generally accepted. The matter was initially very hot, dense, and expanded rapidly. Then the temperature of the Universe dropped to several thousand degrees. The substance at that moment consisted of electrons, protons and alpha particles (helium nuclei), that is, it was a highly ionized gas - plasma, opaque to light and any electromagnetic waves. The recombination (combination) of nuclei and electrons that began at this time, that is, the formation of neutral hydrogen and helium atoms, radically changed the optical properties of the Universe. It became transparent to most electromagnetic waves.
Thus, by studying light and radio waves, one can see only what happened after recombination, and everything that happened before is covered by a kind of “wall of fire” of ionized matter. We can look much deeper into the history of the Universe only if we learn to register relic neutrinos, for which hot matter became transparent much earlier, and primary gravitational waves, for which matter of any density is no barrier, but this is a matter of the future, and far from it. the closest one.
Since the formation of neutral atoms, our Universe has expanded approximately 1,000 times, and the radiation from the recombination era is today observed on Earth as a relic microwave background with a temperature of about three degrees Kelvin. This background, first discovered in 1965 during tests of a large radio antenna, is virtually the same in all directions. According to modern data, there are a hundred million times more relict photons than atoms, so our world is simply bathed in streams of strongly reddened light emitted in the very first minutes of the life of the Universe.
Classical topology of space
On scales larger than 100 megaparsecs, the part of the Universe visible to us is quite homogeneous. All dense clumps of matter - galaxies, their clusters and superclusters - are observed only at shorter distances. Moreover, the Universe is also isotropic, that is, its properties are the same along any direction. These experimental facts underlie all classical cosmological models, which assume spherical symmetry and spatial homogeneity of the distribution of matter.
Classical cosmological solutions to the equations of Einstein's general theory of relativity (GTR), which were found in 1922 by Alexander Friedman, have the simplest topology. Their spatial sections resemble planes (for infinite solutions) or spheres (for limited solutions). But such universes, it turns out, have an alternative: a universe of finite volume that has no edges or boundaries, closed on itself.
The first solutions found by Friedman described universes filled with only one type of matter. Different pictures arose due to differences in the average density of matter: if it exceeded a critical level, a closed universe with positive spatial curvature, finite dimensions and lifetime was obtained. Its expansion gradually slowed down, stopped and was replaced by compression to a point. The Universe with a density below the critical one had a negative curvature and expanded indefinitely, the rate of its inflation tended to some constant value. This model is called open. The flat Universe, an intermediate case with density exactly equal to the critical one, is infinite and its instantaneous spatial sections are flat Euclidean space with zero curvature. A flat one, just like an open one, expands indefinitely, but the speed of its expansion tends to zero. Later, more complex models were invented in which a homogeneous and isotropic universe was filled with multicomponent matter that changed over time.
Modern observations show that the Universe is now expanding at an accelerating rate (see “Beyond the Horizon of Universal Events”, No. 3, 2006). This behavior is possible if space is filled with some substance (often called dark energy) with a high negative pressure, close to the energy density of this substance. This property of dark energy leads to the emergence of a kind of antigravity, which overcomes the gravitational forces of ordinary matter on large scales. The first such model (with the so-called lambda term) was proposed by Albert Einstein himself.
A special mode of expansion of the Universe arises if the pressure of this matter does not remain constant, but increases with time. In this case, the increase in size increases so quickly that the Universe becomes infinite in a finite time. Such a sharp inflation of spatial dimensions, accompanied by the destruction of all material objects, from galaxies to elementary particles, is called the Big Rip.
All these models do not assume any special topological properties of the Universe and present it as similar to our familiar space. This picture agrees well with the data that astronomers obtain using telescopes that record infrared, visible, ultraviolet and X-ray radiation. And only radio observation data, namely a detailed study of the cosmic microwave background, made scientists doubt that our world is structured so straightforwardly.
Scientists will not be able to look beyond the “wall of fire” that separates us from the events of the first thousand years of the life of our Universe. But with the help of laboratories launched into space, every year we learn more and more about what happened after the transformation of hot plasma into warm gas
Orbital radio receiver
The first results obtained by the space observatory WMAP (Wilkinson Microwave Anisotropy Probe), which measured the power of the cosmic microwave background radiation, were published in January 2003 and contained so much long-awaited information that its understanding is not completed today. Physics is usually used to explain new cosmological data: equations of state of matter, expansion laws and spectra of initial perturbations. But this time the nature of the detected angular inhomogeneity of the radiation required a completely different explanation - a geometric one. More precisely, topological.
The main goal of WMAP was to build a detailed map of the temperature of the cosmic microwave background radiation (or, as it is also called, the microwave background). WMAP is an ultra-sensitive radio receiver that simultaneously detects signals coming from two almost diametrically opposite points in the sky. The observatory was launched in June 2001 into a particularly calm and “quiet” orbit, located at the so-called Lagrangian point L2, one and a half million kilometers from Earth. This 840 kg satellite is actually in orbit around the sun, but thanks to the combined action of the gravitational fields of the Earth and the Sun, its orbital period is exactly one year, and it does not fly away from the Earth. The satellite was launched into such a distant orbit so that interference from earthly man-made activity would not interfere with the reception of cosmic microwave background radiation.
Based on the data obtained by the space radio observatory, it was possible to determine a huge number of cosmological parameters with unprecedented accuracy. Firstly, the ratio of the total density of the Universe to the critical density is 1.02±0.02 (that is, our Universe is flat or closed with very little curvature). Secondly, the Hubble constant, which characterizes the expansion of our World on large scales, 72±2 km/s/Mpc. Thirdly, the age of the Universe is 13.4 ± 0.3 billion years and the red shift corresponding to the recombination time is 1088 ± 2 (this is the average value, the thickness of the recombination boundary is significantly greater than the indicated error). The most sensational result for theorists was the angular spectrum of disturbances of the relict radiation, more precisely, the value of the second and third harmonics was too small.
Such a spectrum is constructed by representing the temperature map as a sum of various spherical harmonics (multipoles). In this case, from the general picture of disturbances, variable components are isolated that fit on the sphere an integer number of times: quadrupole 2 times, octupole 3 times, and so on. The higher the number of the spherical harmonic, the more high-frequency background oscillations it describes and the smaller the angular size of the corresponding “spots”. Theoretically, the number of spherical harmonics is infinite, but for a real observation map it is limited by the angular resolution with which the observations were made.
To correctly measure all spherical harmonics, a map of the entire celestial sphere is needed, and WMAP receives its verified version within a year. The first such not very detailed maps were obtained in 1992 in the Relic and COBE (Cosmic Background Explorer) experiments.
How is a bagel similar to a coffee cup?
There is a branch of mathematics - topology, which studies the properties of bodies that are preserved under any deformation without breaks or gluing. Imagine that the geometric body we are interested in is flexible and easily deformed. In this case, for example, a cube or a pyramid can be easily transformed into a sphere or a bottle, a torus (“donut”) into a coffee cup with a handle, but it will not be possible to turn a sphere into a cup with a handle if you do not tear and glue this easily deformable body. In order to divide a sphere into two unconnected pieces, it is enough to make one closed cut, but you can do the same with a torus only by making two cuts. Topologists simply love all sorts of exotic constructions such as a flat torus, a horned sphere or a Klein bottle, which can only be correctly depicted in a space with twice the number of dimensions. Likewise, our three-dimensional Universe, closed on itself, can be easily imagined only by living in six-dimensional space. For a while, cosmic topologists have not yet encroached, leaving it the opportunity to simply flow linearly, without being locked into anything. So the ability to work in the space of seven dimensions today is quite enough to understand how complex our dodecahedral Universe is structured.
The final CMB temperature map is built from painstaking analysis of maps showing the intensity of radio emission in five different frequency ranges
Unexpected decision
For most spherical harmonics, the experimental data obtained coincided with model calculations. Only two harmonics, quadrupole and octupole, were clearly below the level expected by theorists. Moreover, the likelihood that such large deviations could arise by chance is extremely small. Suppression of the quadrupole and octupole was noted in the COBE data. However, the maps obtained in those years had poor resolution and great noise, so discussion of this issue was postponed until better times. For what reason the amplitudes of the two largest-scale fluctuations in the intensity of the cosmic microwave background radiation turned out to be so small was completely unclear at first. It has not yet been possible to come up with a physical mechanism to suppress them, since it must act on the scale of the entire Universe we observe, making it more homogeneous, and at the same time stop working on smaller scales, allowing it to fluctuate more strongly. This is probably why they began to look for alternative paths and found a topological answer to the question that arose. The mathematical solution to the physical problem turned out to be surprisingly elegant and unexpected: it was enough to assume that the Universe is a dodecahedron closed on itself. Then the suppression of low-frequency harmonics can be explained by spatial high-frequency modulation of background radiation. This effect occurs due to repeated observation of the same region of recombining plasma through different parts of a closed dodecahedral space. It turns out that low harmonics seem to cancel themselves due to the passage of the radio signal through different facets of the Universe. In such a topological model of the world, events occurring near one of the faces of the dodecahedron turn out to be close to the opposite face, since these areas are identical and in fact are one and the same part of the Universe. Because of this, the relict light coming to Earth from diametrically opposite sides turns out to be emitted by the same region of the primary plasma. This circumstance leads to the suppression of the lower harmonics of the CMB spectrum even in a Universe only slightly larger in size than the visible event horizon.
Anisotropy map
The quadrupole mentioned in the text of the article is not the lowest spherical harmonic. In addition to it, there are a monopole (zero harmonic) and a dipole (first harmonic). The magnitude of the monopole is determined by the average temperature of the cosmic microwave background radiation, which today is 2.728 K. After subtracting it from the general background, the largest is the dipole component, which shows how much higher the temperature in one of the hemispheres of the space surrounding us is than in the other. The presence of this component is caused mainly by the movement of the Earth and the Milky Way relative to the relict background. Due to the Doppler effect, the temperature in the direction of movement increases, and in the opposite direction it decreases. This circumstance will make it possible to determine the speed of any object in relation to the cosmic microwave background radiation and thus introduce the long-awaited absolute coordinate system, locally at rest in relation to the entire Universe.
The magnitude of dipole anisotropy associated with the Earth's motion is 3.353*10-3 K. This corresponds to the motion of the Sun relative to the CMB background at a speed of about 400 km/s. At the same time, we “fly” in the direction of the border of the constellations Leo and Chalice, and “fly away” from the constellation Aquarius. Our Galaxy, together with the local group of galaxies in which it belongs, moves relative to the relic at a speed of about 600 km/s.
All other disturbances (from the quadrupole and above) on the background map are caused by inhomogeneities in the density, temperature and velocity of matter at the recombination boundary, as well as by the radio emission of our Galaxy. After subtracting the dipole component, the total amplitude of all other deviations turns out to be only 18 * 10-6 K. To exclude the Milky Way’s own radiation (mainly concentrated in the plane of the galactic equator), observations of the microwave background are carried out in five frequency bands in the range from 22.8 GHz to 93 .5 GHz.
Combinations with a torus
The simplest body with a topology more complex than a sphere or plane is a torus. Anyone who has held a bagel in their hands can imagine it. Another more correct mathematical model of a flat torus is demonstrated by the screens of some computer games: it is a square or rectangle, the opposite sides of which are identified, and if a moving object goes down, it appears from above; crossing the left border of the screen, it appears from behind the right, and vice versa. Such a torus is the simplest example of a world with a non-trivial topology, which has a finite volume and does not have any boundaries.
In three-dimensional space, a similar procedure can be done with a cube. If we identify its opposite faces, a three-dimensional torus is formed. If you look from inside such a cube at the surrounding space, you can see an infinite world, consisting of copies of its one and only and unique (non-repeating) part, the volume of which is completely finite. In such a world there are no boundaries, but there are three distinct directions parallel to the edges of the original cube, along which periodic rows of original objects are observed. This picture is very similar to what can be seen inside a cube with mirrored walls. True, looking at any of its faces, an inhabitant of such a world will see the back of his head, and not his face, as in an earthly funhouse. A more correct model would be a room equipped with 6 television cameras and 6 flat LCD monitors, on which the image captured by the film camera located opposite is displayed. In this model, the visible world closes on itself thanks to access to another television dimension.
The picture of suppression of low-frequency harmonics described above is correct if the time it takes for light to cross the initial volume is sufficiently short, that is, if the dimensions of the initial body are small compared to cosmological scales. If the dimensions of the observable part of the Universe (the so-called horizon of the Universe) turn out to be smaller than the dimensions of the original topological volume, then the situation will be no different from what we will see in the usual infinite Einstein Universe, and no anomalies in the spectrum of the cosmic microwave background radiation will be observed.
The maximum possible spatial scale in such a cubic world is determined by the dimensions of the original body; the distance between any two bodies cannot exceed half the main diagonal of the original cube. Light coming to us from the recombination boundary can cross the original cube several times along the way, as if reflected in its mirror walls, because of this the angular structure of the radiation is distorted and low-frequency fluctuations become high-frequency. As a result, the smaller the initial volume, the stronger the suppression of lower large-scale angular fluctuations, which means that by studying the CMB, we can estimate the size of our Universe.
3D mosaics
A flat topologically complex three-dimensional Universe can be built only on the basis of cubes, parallelepipeds and hexagonal prisms. In the case of curved space, a wider class of figures has such properties. At the same time, the best angular spectra obtained in the WMAP experiment are consistent with a model of the Universe having the shape of a dodecahedron. This regular polyhedron, which has 12 pentagonal faces, resembles a soccer ball sewn from pentagonal patches. It turns out that in a space with a slight positive curvature, regular dodecahedrons can fill the entire space without holes or mutual intersections. Given a certain ratio between the size of the dodecahedron and the curvature, this requires 120 spherical dodecahedrons. Moreover, this complex structure of hundreds of “balls” can be reduced to a topologically equivalent one, consisting of just one single dodecahedron, whose opposite faces are identified, rotated by 180 degrees.
The universe formed from such a dodecahedron has a number of interesting properties: it has no preferred directions, and it describes the magnitude of the lowest angular harmonics of the CMB better than most other models. Such a picture arises only in a closed world with a ratio of the actual density of matter to the critical density of 1.013, which falls within the range of values allowable by today's observations (1.02 ± 0.02).
For the average inhabitant of the Earth, all these topological intricacies at first glance do not have much significance. But for physicists and philosophers it’s a completely different matter. Both for the worldview as a whole and for a unified theory that explains the structure of our world, this hypothesis is of great interest. Therefore, having discovered anomalies in the spectrum of the relic, scientists began to look for other facts that could confirm or refute the proposed topological theory.
Sounding plasma
On the spectrum of CMB fluctuations, the red line indicates the predictions of the theoretical model. The gray corridor around it is the permissible deviations, and the black dots are the results of observations. Most of the data is obtained from the WMAP experiment, and only for the highest harmonics results from the CBI (balloon) and ACBAR (ground-based Antarctic) studies are added. The normalized graph of the angular spectrum of CMB fluctuations shows several maxima. These are the so-called “acoustic peaks”, or “Sakharov oscillations”. Their existence was theoretically predicted by Andrei Sakharov. These peaks are due to the Doppler effect and are caused by the movement of the plasma at the moment of recombination. The maximum amplitude of oscillations occurs within the size of the causally related region (sound horizon) at the moment of recombination. On smaller scales, plasma oscillations were weakened by photon viscosity, and on large scales the disturbances were independent of each other and were not phased. Therefore, the maximum fluctuations observed in the modern era occur at the angles at which the sound horizon is visible today, that is, the region of the primary plasma that lived a single life at the moment of recombination. The exact position of the maximum depends on the ratio of the total density of the Universe to the critical one. Observations show that the first, highest peak is located approximately at the 200th harmonic, which, according to theory, corresponds with high accuracy to a flat Euclidean Universe.
A lot of information about cosmological parameters is contained in the second and subsequent acoustic peaks. Their very existence reflects the fact that acoustic oscillations in plasma are “phased” during the recombination era. If there were no such connection, then only the first peak would be observed, and fluctuations on all smaller scales would be equally probable. But in order for such a causal relationship between oscillations on different scales to arise, these (very distant from each other) regions had to be able to interact with each other. This is precisely the situation that naturally arises in the inflationary Universe model, and the confident detection of the second and subsequent peaks in the angular spectrum of CMB fluctuations is one of the most significant confirmations of this scenario.
Observations of the cosmic microwave background radiation were carried out in the region close to the maximum of the thermal spectrum. For a temperature of 3K it is at a radio wavelength of 1mm. WMAP conducted its observations at slightly longer wavelengths: from 3 mm to 1.5 cm. This range is quite close to the maximum, and it contains lower noise from the stars of our Galaxy.
Multifaceted world
In the dodecahedral model, the event horizon and the recombination boundary lying very close to it intersect each of the 12 faces of the dodecahedron. The intersection of the recombination boundary and the original polyhedron forms 6 pairs of circles on the microwave background map, located at opposite points of the celestial sphere. The angular diameter of these circles is 70 degrees. These circles lie on opposite faces of the original dodecahedron, that is, they coincide geometrically and physically. As a result, the distribution of CMB fluctuations along each pair of circles should coincide (taking into account the rotation by 180 degrees). Based on the available data, such circles have not yet been detected.
But this phenomenon, as it turned out, is more complex. The circles will be identical and symmetrical only for an observer stationary relative to the relict background. The Earth moves relative to it at a fairly high speed, which is why a significant dipole component appears in the background radiation. In this case, the circles turn into ellipses, their sizes, location in the sky and the average temperature along the circle change. It becomes much more difficult to detect identical circles in the presence of such distortions, and the accuracy of the data available today becomes insufficient; new observations are needed that will help figure out whether they exist or not.
Multiply related inflation
Perhaps the most serious problem of all topologically complex cosmological models, and a considerable number of them have already arisen, is mainly of a theoretical nature. Today, the inflationary scenario for the evolution of the Universe is considered standard. It was proposed to explain the high homogeneity and isotropy of the observable Universe. According to him, at first the Universe that was born was quite heterogeneous. Then, during the process of inflation, when the Universe expanded according to a law close to exponential, its original size increased by many orders of magnitude. Today we see only a small part of the Big Universe, in which inhomogeneities still remain. True, they have such a large spatial extent that they are invisible within the area accessible to us. The inflationary scenario is the best developed cosmological theory so far.
For a multiconnected universe, such a sequence of events does not fit. In it, all of its unique part and some of its closest copies are available for observation. In this case, structures or processes described by scales much larger than the observed horizon cannot exist.
The directions in which cosmology will have to be developed if the multiconnectedness of our Universe is confirmed are already clear: these are non-inflationary models and so-called models with weak inflation, in which the size of the Universe increases only a few times (or tens of times) during inflation. There are no such models yet, and scientists, trying to preserve the familiar picture of the world, are actively looking for flaws in the results obtained using a space radio telescope.
Processing artifacts
One of the groups that conducted independent studies of WMAP data drew attention to the fact that the quadrupole and octupole components of the CMB have a close orientation to each other and lie in a plane almost coinciding with the galactic equator. The conclusion of this group: an error occurred when subtracting the Galactic background from the microwave background observation data and the real value of the harmonics is completely different.
WMAP observations were carried out at 5 different frequencies specifically in order to correctly separate the cosmological and local background. And the core WMAP team believes that the observations were processed correctly and rejects the proposed explanation.
The available cosmological data, published back in early 2003, were obtained after processing the results of only the first year of WMAP observations. To test the proposed hypotheses, as usual, an increase in accuracy is required. By early 2006, WMAP had been continuously observing for four years, which should be enough to double its accuracy, but the data has yet to be published. We need to wait a little, and perhaps our assumptions about the dodecahedral topology of the Universe will become completely demonstrative.
Mikhail Prokhorov, Doctor of Physical and Mathematical Sciences
Ecology of life. Science and Discovery: People have debated why the universe exists for thousands of years. In almost every ancient culture, people came up with their own...
Some physicists believe they can explain how our Universe formed. If they turn out to be right, then our cosmos could arise from nothing.
People have been debating why the universe exists for thousands of years. In almost every ancient culture, people came up with their own theory of creation - most of them included divine design - and philosophers wrote many volumes about it. But science can tell only so much about the creation of the Universe.
However, recently some physicists and cosmologists have begun to debate this issue. They note that we now have a good understanding of the history of the Universe and the laws of physics that explain how it works. Scientists believe that this information will allow us to understand how and why space exists.
In their opinion, the Universe, from the Big Bang to our multi-stellar cosmos that exists today, arose from nothing. This had to happen, scientists say, because “nothing” is actually internally unstable.
This idea may seem strange or simply fabulous. But physicists say it comes from two of the most powerful and successful theories: quantum physics and general relativity.
So how could everything come from nothing?
Particles from empty space
To begin with, we should turn to the field of quantum physics. This is a branch of physics that studies very small particles: atoms and even smaller objects. Quantum physics is an extremely successful theory and has become the foundation for most of today's electronic gadgets.
Quantum physics tells us that empty space does not exist at all. Even the most ideal vacuum is filled with a rippling cloud of particles and antiparticles that appear from nothing and then turn into nothing. These so-called “virtual particles” exist for a short time and therefore we cannot see them. However, we know they are there because of the effects they cause.
To space and time from the absence of space and time
Let's now shift our focus from the smallest objects - such as atoms - to very large things - such as galaxies. Our best theory for explaining such big things is general relativity, Albert Einstein's crowning achievement. This theory explains how space, time and gravity are interconnected.
General relativity is very different from quantum physics, and until now no one has been able to put them together into a single puzzle. However, some theorists have been able to use carefully chosen similarities to bring the two theories closer to each other in specific problems. For example, this approach was used by Stephen Hawking at the University of Cambridge when he described black holes.
Physicists have discovered that when quantum theory is applied to space on small scales, space becomes unstable. Space and time, instead of remaining smooth and continuous, begin to seethe and foam, taking the form of bursting bubbles.
In other words, small bubbles of time and space can form spontaneously. “In the quantum world, time and space are unstable,” says astrophysicist Lawrence Maxwell Krauss of Arizona State University. “So you can shape virtual spacetime in the same way that you shape virtual particles.”
Moreover, if these bubbles can occur, you can be sure that they will occur. “In quantum physics, if something is not forbidden, it will definitely happen with a certain degree of probability,” says Alexander Vilenkin from Tufts University in Massachusetts.
Universe from a bubble
So, not only can particles and antiparticles come from nothing and turn into nothing: bubbles of spacetime can do the same thing. However, there is a large gap between the infinitesimal space-time bubble and the vast Universe, consisting of more than 100 billion galaxies. Indeed, why shouldn’t a bubble that has just appeared disappear in the blink of an eye?
And it turns out there is a way to make the bubble survive. This requires another trick called cosmic inflation.
Most modern physicists believe that the Universe began with the Big Bang. At first, all the matter and energy in space was compressed into an incredibly small point, which then began to expand rapidly. Scientists learned that our Universe is expanding in the 20th century. They saw that all the galaxies were flying away from each other, which means that they were once located close to each other.
According to the inflationary model of the Universe, immediately after the Big Bang the Universe expanded much faster than it does today. This outlandish theory emerged in the 1980s, thanks to Alan Guth of the Massachusetts Institute of Technology, and was refined by Soviet physicist Andrei Linde, now at Stanford University.
The idea behind the inflationary model of the Universe is that immediately after the Big Bang, a small bubble of space expanded at an enormous rate. In an incredibly short period of time, from a point smaller in size than the nucleus of an atom, it reached the volume of a grain of sand. When the expansion eventually slowed, the force that caused it was transformed into the matter and energy that fill the Universe today.
Despite its apparent strangeness, the inflationary model of the Universe corresponds well to the facts. In particular, it explains why the cosmic microwave background radiation - the cosmic microwave background radiation left over from the Big Bang - is evenly distributed in the sky. If the Universe were expanding not so quickly, then, most likely, the radiation would be more chaotic in distribution than we see today.
The Universe is Flat and Why This Fact Is Important
Inflation also helps cosmologists determine the geometry of our Universe. It turned out that knowledge of geometry is necessary to understand how the cosmos could arise from nothing.
Albert Einstein's general theory of relativity says that the space-time in which we live can take three different forms. It can be flat, like the surface of a table. It can be curved, like the area of a sphere, and therefore, if you start moving from a certain point, you will definitely return to it. Finally, it can be turned outward, like a saddle. So what form of space-time do we live in?
This can be explained as follows. You may remember from school math lessons that the angles of a triangle add up to 180 degrees. This is only true when the triangle is in flat space. If you draw a triangle on the surface of a balloon, the sum of the three angles will add up to more than 180 degrees. If you draw a triangle on a surface like a saddle, the sum of the three angles will be less than 180 degrees.
In order to understand that our Universe is flat, we need to measure the angles of a giant triangle. And this is where the inflationary model of the Universe comes into play. It determines the average sizes of cold and hot spots in the cosmic microwave background. These spots were measured in 2003, and it was them that astronomers were able to use as analogues of the triangle. As a result, we know that the largest observable scales in our Universe are flat.
Thus, it turns out that a flat Universe is a necessity. This is true because only a flat Universe could have formed from nothing.
Everything that exists in the Universe, from stars and galaxies to the light they produce, must have been formed from something. We already know that particles arise at the quantum level, so we might expect that there are some little things in the Universe. But the formation of all these stars and planets requires a huge amount of energy.
But where did the Universe get all this energy? It sounds strange, of course, but the energy didn’t have to come from somewhere. The fact is that every object in our Universe has gravity and attracts other objects to itself. And this balances the energy required to create the first matter.
It's a bit like an old scale. You can put an arbitrarily heavy object on one pan of a scale, and the scale will be in balance if there is an object of the same mass on the other end. In the case of the Universe, matter is located at one end, and gravity “balances” it.
Physicists have calculated that in a flat Universe, the energy of matter is exactly equal to the gravitational energy that this matter creates. But this only works for a flat Universe. If the Universe were curved, there would be no balance.
Universe or multiverse?
Now, "cooking" the Universe looks quite simple. Quantum physics tells us that “nothing” is unstable, and therefore the transition from “nothing” to “something” must be almost inevitable. Further, thanks to inflation, a massive, dense Universe can be formed from a small space-time bubble. As Krauss wrote, “The laws of physics, as we understand them today, allow that our universe formed out of nothing—there was no time, no space, no particles, nothing of which we are aware.”
But why then did the Universe form only once? If one bubble inflated to the size of our Universe, why can't other bubbles do the same?
Linde offers a simple but psychedelic answer. He believes that the Universes have arisen and are arising continuously, and this process will continue forever.
When the inflation of the Universe ends, Linde believes, it still continues to be surrounded by space in which inflation exists. It causes the emergence of even more Universes, and around them even more space is formed in which inflation occurs. Once inflation starts, it will continue indefinitely. Linde called this eternal inflation. Our Universe may be just a grain of sand on an endless sandy beach.
Other universes may be very different from ours. The neighboring universe may have five spatial dimensions, while ours has only three - length, width and height. The force of gravity in it can be 10 times stronger or 1000 times weaker. Or there may be no gravity at all. Matter can consist of completely different particles.
Thus, there may be a diversity of Universes that does not fit into our consciousness. Linde believes that perpetual inflation is not just a “totally free lunch,” but it is also the only lunch where every possible dish is available. published
Translation: Ekaterina Shutova
