Our imagination can be very great but it always takes elements from what is already known to generate its creative visions, after all how is it possible to imagine something that does not even have a presence in the mental structure? It is for this reason that most people, if not all, have problems with the abstraction of concepts that escape our small world. The Universe is one of these concepts that we are not able to imagine, because it is so complex and intricate that the only way we have to understand it is the data collected from our telescopes and mathematics. With these two powerful tools we have enough evidence to get a vague idea of what the true shape of the Universe is. Is it flat, curved, cubic or doughnut-shaped?
The Cosmological Principle
The answer to the geometry of the Universe is hidden in the equations of the Theory of the great Albert Einstein. However, they are too complicated to embark on an adventure without head or tail. This is why before starting to wander aimlessly in a world of numbers, what scientists do first is think about helping them establish a guide to know where to look.
In search of answers, in 1922 the Russian Aleksandr Friedmann formulated two simple, although very important hypotheses about our Universe. The first is that the Universe is homogeneous, that is, no matter where you look on colossal scales, the Universe always seems the same in any direction, at least statistically speaking. The second hypothesis is that the Universe is isotropic, which would be intrinsically linked to the previous one. This tells us that the Universe is homogeneous, no matter what point of observation it is viewed from, it does not matter if we look from it or from a galaxy millions of light years away; We will always see a homogeneous Universe.
Of course, this does not apply to small scales like the ones our minds are used to thinking about. Of course, observing the Milky Way is not the same as analyzing Andromeda, but we are talking on much larger scales. It’s like looking at human skin, if we look at it under a microscope we will discover that it is made up of different types of cells, textures and shapes. However, if we look at it from above, we will see the same thing everywhere, only skin.
These two hypotheses, that the Universe is homogeneous and isotropic, make up what astrophysicists call the Principle, which says that there is no region of the cosmos that is special or different. That is, there are no privileged sections that are governed by special or unique laws. The famous principle is widely recognized by researchers not only because it works philosophically speaking because it makes us understand that we are nothing and at the same time a whole in reality; but it also gives us answers mathematically speaking, since it is conclusive with the evidence that has been obtained from the cosmic microwave background.
Know what it is not to understand what it can be
From here and based on the Cosmological Principle, physicists began to discard those geometries that do not fit with a uniform Universe and thus discover its true form. All geometry that does not align with homogeneity is discarded, which is why we know that the Universe cannot be cubic or any other shape that has strange edges.
What do we have left? Only those geometries where each place is exactly the same as any other or, mathematically speaking, shapes with uniform curvature, any ideas? It seems very abstract and in fact it is, but the simplest forms that adhere to these characteristics are those of a spherical, flat Universe or with strange geometries such as hyperbolic spaces, which are basically homogeneous figures but with strange curvatures, like a chair. riding.
What do the angles tell us?
At school we learned Euclidean geometry, which is geometry that develops in a two-dimensional plane. However, when talking about the Universe, nothing is so simple and now instead of thinking about shapes in a two-dimensional space, we must do so in a space with three axes, that is, three dimensions, therefore, Euclidean geometry is not the only one that exists.
In that sense, we can imaginatively draw a triangle over the candidate geometries of the Universe and by measuring its angles and adding them, we will discover which reality we fit into. There are three possible results, the first is that the sum is equal to 180º, in which case we would be talking about a flat Universe. If the sum exceeds 180º then we speak of a spherical Universe, but if it is less than this, then we must think that it is a hyperbolic Universe.
*Example of a triangle on a hyperbolic Universe and why the sum of its angles would be less than 180º.
But we still have the question of how do we draw and measure an imaginary triangle over the vast Universe? The detection of microwave background radiation gave us many answers and this is one of them. When the Big Bang occurred, an enormous amount of radiation was ejected in all directions and although that was more than 13.7 billion years ago, the Universe is so large that that light is still traveling around and we can detect it.
A flat and expanding Universe
Microwave background radiation gives us many data about the Universe and its mysteries. One of them is precisely that its shape is consistent with a flat Universe. However, although most evidence points to it having a planar geometry, this does not necessarily mean that its topology is.
*Microwave Background Radiation.
Topology would help us understand how the points within this Universe are connected and one of the questions that will help us understand this issue has to do with return points. If we start walking in a straight line through this flat Universe, is it possible that at some point we will return to the same point where we started? In that sense, a space with flat geometry (remember that we are not talking about two dimensions), can have a donut topology. In this case, whether we circled the donut vertically or horizontally, we would always arrive at the same point.
This donut shape is consistent with the Principle of Cosmology and with a Universe of flat geometry, however, it is not the only possibility and, in fact, it has been discarded by many cosmologists. On the other hand, physicists believe that there is another possible scenario where there are no return points, that of a flat but infinite Universe. One where no matter how much you walk in the same direction, you will never reach the same point where you started. And this is where other theories come into question that reinforce the idea that y has an infinite topology that expands without control.
Albert Einstein’s cosmological constant and dark energy are just some of the theories that reinforce the idea that our Universe is flat, infinite and expanding, although explaining why is material for another occasion, as is the curvature. of space which is not the same as the geometry of the Universe.