Accelerated expansion of the Universe

In 1927-29, Edwin Hubble (1889-1953) and Georges Lemaitre (1894-1966) observed that the Universe was expanding. All galaxies are moving away from us and distant galaxies are moving away from us faster than nearby galaxies. This observation means that space is growing. Everything happens as if the Universe were growing from within!
This is enough to say that our Universe is expanding because if it were the galaxies that were moving, we could not explain this observation.
The expansion of the Universe is therefore a rather disturbing phenomenon, because the galaxies without moving, move away from each other and there is no contradiction to this observation. Since the 1990s, observations have convincingly shown that the expansion of the universe is accelerating, rather than slowing down as one would expect due to the gravitational pull between galaxies. Data collected from various observational methods, including supernovae, cosmic rays, and baryon acoustic oscillations (BAO), have all confirmed this finding. We even know the accelerated expansion speed which is 72 km/s/Mpc. General relativity predicts that expansion must slow down over time because matter tends to slow down expansion. Which means that in the past the speed must have been faster than today. Another oddity is that this speed measured over time does not correspond to the predictions. The speed of expansion increases over time. She was smaller in the past than she is today. More precisely, during the first 8 billion years of the evolution of the Universe, the speed of expansion decreases over time as expected and then suddenly it accelerates.
So what is driving this acceleration that started 5 billion years ago?
Scientists for more than 20 years have developed many theories. However, despite the many theories that attempt to explain this oddity, we still do not know what is the phenomenon responsible for the accelerated expansion of the Universe. Theories are classified into two different categories, those of dark energy and those of modified gravity.
The main hypothesis to explain this acceleration is the existence of dark energy. Unlike ordinary matter, this form of energy should not be diluted in a volume growing over time but should remain evenly distributed throughout the universe. When the Universe grows the amount of dark energy must also grow proportionally. When the amount of dark energy grows the universe grows and therefore there is more dark energy. This cycle forces the Universe to expand faster and faster!

One of the most popular hypotheses is that dark energy is simply a cosmological constant, a form of energy whose density remains constant over time and throughout the universe. Dark energy accounts for nearly 70% of all energy density in the universe. That's a lot, but by tinkering with the cosmological constant, that is to say by giving it the right value, we can obtain a Universe that begins to accelerate the first 8 billion years after the Big Bang. However, this is not satisfactory. The nature of dark energy is still largely unknown. In the categories explaining dark energy we find the theories of Gauss-Bonnet, Brans-Dicke, Einstein-Aether, Bigravity, Cascading gravity, The Fab Four, Galileon, Massive gravity, Randall-Sundrum, etc.
Another hypothesis is that the acceleration of the expansion of the universe can be explained by a modification of gravity on a very large scale. This theory proposes that gravity does not exactly follow Newton's laws at very large scales, and that this may explain the acceleration of the expansion of the universe.
Indeed general relativity has been enormously tested and validated but never on a very large scale, that of the entire Universe. In this category of modified gravitation we find the theories of Quintessence, K-essence, Phantom dark energy, Coupled quintessence, Cosmological constant, Chaplygin gas, etc.
Ultimately, we don't yet know the true nature of dark energy and the accelerating expansion of the universe. Physicists are trying to test these two paradigms capable of explaining the observations, that of dark energy and that of modified gravitation. This would eliminate a group of theories. The Euclid or SKA missions will help to decide between these two groups of theories.
Professor Camille Bonvin, professor at the University of Geneva, has developed a method to test these two paradigms. It consists in comparing the distortion of time and the distortion of space, generated by the galaxies and clusters present in the Universe. Einstein's general relativity predicts that these two distortions are equal, unlike alternative theories of gravity in which, generally, these distortions differ.
Testing the validity, at the edge of the Universe, of Einstein's theory is undoubtedly one of the major challenges of tomorrow's cosmology.