Vicious Circle: How the Universe can be finite and have no edge

The observable universe stretches for about 92 billion light-years across, but this does not allow us to determine the size of the entire cosmos. Measurements show that the area of space available to us is almost flat. At the same time, the universe can continue indefinitely, have a weak curvature on scales inaccessible to observation, or lock itself in. What is known about its shape and why the answer to the question of infinity remains open is in the "Izvestia" material.

Where does the observable universe end?

When astronomers talk about the size of the observable universe, they mean the area from which light has managed to reach us. According to NASA estimates, its diameter is about 92 billion light-years. This does not contradict the fact that the age of the universe is estimated at about 13.8 billion years: as the light flew towards the Earth, space expanded, and the distance to the regions that emitted it increased.

But the boundary of the observed area does not look like a wall or an edge. It means the limit of information available to us. There may be other galaxies and vast spaces beyond it, but their existence and properties cannot be established simply by continuing observations.

The first value is finite: it can be estimated. For the second, science does not yet have a reliable estimate. As NASA notes, it is not even known whether the universe as a whole is finite.

How can a finite space exist without an edge

Intuition tells us that everything finite should have a boundary. The surface of the Earth shows why this is not necessarily the case. Its area can be measured, but a traveler who moves along the surface in one direction will not find the place where it ends. If you continue walking long enough, you can return to the starting point.

Of course, the earth's surface is two-dimensional, and the space around us has three dimensions. Therefore, we are talking about an analogy that allows us to imagine a finite space without an edge, and not about the assumption that the universe is literally arranged like the surface of a planet.

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The curvature of the surface can be detected by staying on it. For example, the sum of the angles of a large triangle built on a sphere will be greater than 180 degrees. Paths heading north from different points of the equator will converge at the pole. On a regular plane, the geometry behaves differently.

Scientists are looking for similar signs on the scale of space. If space is curved, it affects how light propagates and how distant objects are seen. One of the most important sources of information for such measurements is cosmic microwave background radiation.

What did the ancient light tell us about the shape of space

The cosmic microwave background radiation originated in the early universe, when matter cooled sufficiently and light could spread freely. Today it is observed as a faint microwave glow coming from all directions. Small temperature differences are visible on his map, reflecting the inhomogeneities of the young universe.

There is a kind of cosmic "ruler" in this picture. Before light began to spread freely, fluctuations appeared in the hot matter of the early universe. Physical models allow us to estimate their characteristic size. The researchers then compare the calculation with how large the corresponding areas look in the sky. The curvature of space would affect their apparent angular size. This method helps to check whether the space corresponds to a flat geometry.

The results of the observations are in good agreement with the almost flat space. In particular, a joint analysis of data from the Planck Space Observatory and measurements of the distribution of galaxies gave a value of the curvature parameter compatible with zero within the margin of error. This is a strong argument in favor of the fact that the observable region of the universe is very close to geometrically flat. But measuring with finite precision cannot prove that the curvature is strictly zero everywhere.

Why is a flat Universe not necessarily infinite?

Even the Earth seems flat if you examine a fairly small area of its surface. The curvature becomes noticeable only when measured at much greater distances. Sutter draws attention to a similar limitation of cosmological observations: the area available to us may be too small compared to the entire universe to detect a very weak curvature.

But there is a more unexpected option. A space can be flat in terms of geometry and at the same time enclose itself. It is important to distinguish between geometry and topology here. The first one describes, in particular, the curvature of space. The second is how its areas are interconnected.

The simplest two—dimensional analogy is a piece of paper. If you mentally connect its opposite edges, you can get a surface on which movement in one direction leads back to the starting point. At the same time, the small triangles on it still obey the rules of the plane geometry. In three dimensions, the mathematical description of such spaces is more complicated, but the general principle remains the same: the absence of curvature alone does not answer the question of whether space has a finite volume.

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One of the variants of such a device is a three—dimensional torus. It is convenient to imagine it not as an ordinary bagel, but as a space in which the opposite sides of an imaginary cube are connected to each other. Moving through one side, the observer in this model would return from the opposite side. This is a mathematical possibility, not an established form of our universe.

Have astronomers been looking for signs of a "closed" Universe

If light can travel through space in different ways and return to an already visible area, the same space object is theoretically capable of appearing in different parts of the sky. Another possible sign is the matching drawings on the relic radiation map. For some models of an enclosed space, researchers are looking for pairs of circles with similar temperature patterns.

Convincing confirmation of such repeats has not yet been found. Analysis of the Planck data revealed no signs of a closed topology in the models studied and at the scales to which this method is sensitive. However, the absence of a signal does not exclude all possible spatial arrangements: the characteristic size of a closed area may exceed the observable scale, and some forms of topology are more difficult to recognize.

Researchers have shown that previous searches for repetitive patterns leave open many options for the shape of space. More complex connections between its regions can create signals that do not look like simple identical images. This is not proof of a closed universe, but an indication of the limits of the checks already carried out.

So far, observations allow us to confidently talk about the properties of the part of space available to us.: it is huge and on the studied scales it is close to geometrically flat. This does not imply an unambiguous conclusion about the size of the entire space. It may extend far beyond the cosmic horizon, have a curvature too weak for current measurements, or have a structure in which its different regions are interconnected.

New measurements are able to narrow down the range of acceptable models and detect signs of topology that previously went unnoticed. But if the features of the universe's structure manifest themselves only far beyond the region from which information can come to us, there may be no direct answer.