**If you think of the universe on a large scale, the universe as a whole, what do you think of?** In a giant sphere? On an infinite plane? Maybe in a donut, a triangle or an icosahedron? **The answer to this question is incredibly important** , and has kept countless scientists awake for decades.

**We tend to imagine outer space** , the space occupied by our solar system, our galaxy and the rest of the objects that populate the universe **as the place where things happen** , as if it were a backdrop of no real importance for the theatrical representation that would be the history of the universe. However, **general relativity tells us that space is a physical entity** . In fact, **Einstein’s equations of general relativity tell us about two entities that** are just as important and just as real: **the energy content of the universe** (that is, its mass and energy) **and the space-time that contains that energy** . These equations therefore tell us that it is **energy** (and mass, they are equivalent) **that tells space how it should curve and that it is the curvature of this space that tells energy** (and mass, again) **how should it move**

Therefore, mass and energy curve spacetime (this is how we understand gravity since Einstein proposed this theory) and **this spacetime is even capable of vibrating** , as a consequence of the rapid movement of masses, **in the form of gravitational waves** . But all this tells us about **the local curvature of the universe** , about the curvature at a very specific point, such as **in the vicinity of a black hole, in the core of the Sun or in intergalactic space** . In addition to the local curvature, **we can also talk about the global curvature of the universe, its shape** .

You can think of it this way: **imagine you have a fairly rough, flexible sheet of wood** . On a global scale, **you can leave that sheet flat** , if for example you use it for a table top, **or you can give it a certain curvature** , if it is part of a larger and more elaborate structure. But **on a microscopic scale** , the sheet will have a changing curvature on every square millimeter of its surface. In some pieces **the imperfections will be more pronounced and in others not so much** . Something similar happens in the universe.

The best way to summarize the different properties of space is to understand its curvature. In a **flat, uncurved** space (or region of space), two objects moving in parallel will keep moving in parallel forever. In a space with **positive curvature** , such as near a planet or star, two objects that were going in parallel can collide and in a space with **negative curvature** , these same objects will move away to infinity.

There are several ways to measure the curvature of the universe, one of them is **by measuring its energy density, that is, by measuring its mass and energy content** , or how full it is. **If the energy density of the universe is very large** , then gravity due to all the mass present **will cause the expansion of the universe resulting from the Big Bang to stop in the future** , then the universe will contract until all its contents are once again concentrated in a point. **If the energy density is very small, then gravity will not be able to stop this expansion and the universe will continue to expand forever** , never stopping. Finally, if the energy density of the universe **is equal to a specific value, gravity will be able to stop the expansion of the universe, but it will take an infinite time to do so** , so this expansion will slow down and stop, but within an infinitely long time.

Experiments carried out in the last two decades, such as **the study of the cosmic microwave background by the WMAP or Planck probes, clearly show us that the energy density is very close to the critical value necessary to have a flat universe** . These same observations allow us, together with other independent studies, to determine the content of the universe, discovering that only **5% of it corresponds to the matter that we call baryonic** , the ordinary matter that makes up our body, planet, star and our galaxy. The rest would be **24% dark matter** and **71% dark energy** . This dark energy, whose nature we currently do not know, has the effect of accelerating the expansion of the universe (remember that in a flat universe this expansion slows down slowly), so we seem to **live in a specific historical moment in which the curvature global of the universe is 0** , that is, it is flat, but in the future this curvature could become negative, accelerating the expansion of the universe more and more.

Future research that is even more precise, and future theoretical models that are even more complete, will hopefully shed light on these issues. And when this happens, we will be here to tell you about it.

**REFERENCES:**

Planck Collaboration, 2020, Planck 2018 results. I. Overview and the cosmological legacy of Planck, Astronomy and Astrophysics. 641: A1, doi: 10.1051/0004-6361/201833880