# Einstein wins again: General Relativity confirmed on cosmological scales

“Understanding why the expansion of the Universe today is increasing its speed is probably the most fascinating question in modern cosmology” **Luigi Guzzo**, Professor of Cosmology at the Università Statale di Milano and associated researcher at INAF and INFN, says. He is co-author of an article that appeared today on **Nature Astronomy** where the two most viable hypotheses for the origin of the acceleration are tested: while the standard interpretation implies the existence of a “dark energy” to be added to Einstein equations, the observed acceleration may instead signal an incompleteness in the theory of General Relativity, requiring a deeper modification of the equations themselves.

Using an innovative forward-modelling approach based on numerical simulations, researchers at the Universities of Durham (UK) and Milano (I) have shown that the second hypothesis is hardly viable. In fact, even a small modification to General Relativity leads to a Universe in which galaxies are clustered and move in a way which is significantly at variance with the experimental data. This result strongly remarks the need of the mysterious dark energy, as the propeller of cosmic acceleration.

The **theory of General Relativity**, formulated in 1915, has passed brilliantly all tests so far. Last but not least, the spectacular detection of gravitational waves. If then this is the correct theory of gravity, the discovery that the expansion rate of the Universe is larger today than 7 billion years ago (which deserved the 2011 Nobel Prize in Physics), requires the addition of an extra ingredient in the cosmic mix, the so-called cosmological constant. This introduces a “dark energy” in Einstein equations, corresponding to a repulsive force that counteracts the gravity force produced by matter.

The observed acceleration, however, could signal something more profound, i.e. a breakdown of Einstein’s theory when applied on such enormous scales, where direct tests do not exist yet. In such a case, there might not be the need for dark energy. In a sense, it would be like we were trying to fit the Universe with a dress that is too tight: in this analogy, the dress (standard general relativity) would get over-stretched and would try to get back to its normal size, generating the accelerating pull. How can we then understand whether we need to buy a new dress or accept it as it is, extra-coloured by dark energy?

One way was indicated in 2008 in another Letter to Nature: if we modify the laws of gravity to accommodate the accelerated expansion, we also change the rate at which large-scale structures inside the Universe aggregate in time; galaxies follows this growth and move towards massive regions, with velocities that we know depend directly on the theory that describes gravity. “In our 2008 paper (Nature 451, 541), we showed that the effect of these velocities on the tri-dimensional maps of the galaxy distribution could be used as the fingerprint of possible modifications of the theory of gravity on large scales”, Guzzo says.

“In this new work we have applied this concept to the fullest, using the largest of such maps, the Sloan Digital Sky Survey (SDSS), which has the advantage of including detailed physical information on each galaxy, in particular its total mass in stars”, says Jianhua He, of Durham University and former postdoc at INAF Milano, first author of the article. “This has allowed us to reproduce the same type of galaxies in our computer-simulated Universes, as to make a coherent comparison with the observational data. The novelty of this approach is that it enables us to push the comparison to scales where the traditional approach fails.”

Dr. He and collaborators simulated the distribution and velocities of galaxies in the standard case of a Universe in which General Relativity describes the gravity force, together with the least unnatural variant of this theory, a so-called “f(R) model”. The key result is that the standard model (which includes dark energy through the famous cosmological constant) reproduces the statistical distribution of galaxy positions and velocities in a surprising accurate way. Conversely, the predictions of the slightly modified gravity model depart significantly from the experimental data.

General relativity is thus once more confirmed to be right, and as a consequence dark energy is a necessary ingredient to describe the behaviour of our Universe. Yet we have no idea of what it is, whether it may have something to do with the energy of vacuum, if it is really a constant or an evolving scalar field. These open and fascinating questions drive the next generation of surveys dedicated to building large-scale maps of the galaxy and dark matter distributions. This is in particular the case of the Euclid mission of the European Space Agency (ESA), a satellite to be launched in 2022, in which the Italian community and the Italian Space Agency (ASI) play a primary role.

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