Back in the days when people thought the earth was flat, it was heresy to assume that a long journey in a straight line would eventually lead you back to your starting point. But it's true: walk, fly, swim 40,000 kilometers in one direction and you will be back where you started. And then you wonder: is it possible to do the same trick in space? If you take a rocket that can fly fast enough and long enough without colliding with distant stars or galaxies, can you end up returning to your departure point?
At first glance, this may seem crazy, but in reality it is not. You might think that the universe is infinite and goes on forever in all directions, but we have evidence that the shape and size of the universe is quite finite. First, only 13.8 billion years have passed since the Big Bang, and we can observe the volume of space that light has visited in 13.8 billion years, highlighting each point visited. Secondly, there are hundreds of billions of galaxies that were younger in the past, and the further into the past we look, the more pronounced this becomes. Could it be that one (or more) of these galaxies is the youthful version of the Milky Way we grew up in? Finally, just as the Earth has two dimensions in which we can move on it (from north to south and from west to east, but not from top to bottom),can the Universe be a multidimensional structure (hypersphere or hypertor), in which many dimensions are closed and limited, twist into themselves?
If so, if you walked in a straight line long enough, you would eventually get back to where you started. And if you were immortal, you could one day be able to see the back of your own head just by looking for quite some time, as your eyes will eventually see light reflected from your own back of the head. Well, if the universe really is, how do we know for sure?
To do this, we need to look at the universe at its largest scale and find the places where it has the same properties in all directions. A finite and swirling universe would mean that the same structures appear over and over again. While most of the universe will be difficult to define as swirling, since the limited speed of light means that we will see the same objects at different stages of their evolution (like the younger Milky Way), there will always be objects that will be at the same stage of evolution in different places. The large-scale structure of the Universe does not show such structures, but we have an even better place to look: the cosmic microwave background.
The Big Bang afterglow fluctuations have very specific repeating patterns, but also show a random distribution of these patterns. Many algorithms have been developed to search for repetitive non-random signals in the correlations of fluctuations in different parts of the sky. If the universe were finite and twisted - if parts of it were repeated elsewhere - it would be reflected in the cosmic microwave background.
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But the absence of observed repeating structures does not mean that the universe does not have this type of topology. This means that if the Universe does repeat itself, representing a closed hypersurface, and we can theoretically end up at the same point, moving in a straight line long enough, but this will be noticeable on scales that are larger than the part we observe. Given that we are limited by the distance that light has traveled in 13.8 billion years, such a scenario is quite possible.
But there is one but.
No matter how technically advanced we are, one day in the future, as long as we are limited by the speed of light, we will never know if the universe actually behaves this way. Thanks to dark energy and the accelerated expansion of the universe, it is physically impossible to reach the border of even the current observable universe; we can cover a third of this way at most. If the universe does not repeat itself on scales that are less than 15 billion light-years of modern diameter, we will never return to the point where we started in a straight line.
But this does not mean that the Universe cannot be closed, finite, and twist into a hypersphere. This means that the expansion of the Universe - accelerated expansion - prohibits us from "circumnavigating the globe" in the Universe. Due to a combination of factors such as:
- the final age of the Universe;
- the final speed of light;
- expansion of the Universe;
- and the presence of dark energy, we may never know whether our Universe is infinite or not, and what its true topology is.
All that we can see is the part available to us that allows us to set limits on the possible topology of the universe. As far as we can tell, it is flat, non-repeating, and possibly, but not necessarily, infinite. Perhaps, as time passes, when the Universe will open up to us more and more, our measurements of curvature will become more and more accurate and reveal to us a new truth. Despite the fact that we are severely limited in our ability to observe, there may be new, as yet unknown opportunities for the cosmic horizon.
ILYA KHEL