When glancing at the night sky, we admire the arabesques of distant galaxies. It is hard to grasp that these galaxies are moving away from us, pulled by the expansion of the Universe. Even less intuitively, our observations have shown that this expansion is getting faster and faster. Why? This is one of the main open questions of cosmology, the branch of physics that studies the Universe as a whole. 

 

According to the standard cosmological model, this acceleration is due to a mysterious form of repulsive “dark energy”, which constitutes around 70% of the Universe. However, cosmologists are not satisfied with wandering in darkness and are searching for alternative explanations. A well-investigated possibility is that, on very large scales, the laws of gravity could be different from what we observe on Earth, leading to the observed acceleration. 

 

To understand this hypothesis, let us take a stroll in the realm of General Relativity, our current theory of gravity developed by Albert Einstein. General Relativity states that gravity is not a force, but rather a deformation of space and time. We can picture the Universe as a tablecloth that gets distorted by objects with a mass, creating deformations called “gravitational potentials”. The path of any particle traveling across the tablecloth is deviated by these potentials. 

 

The predictions of General Relativity have been verified by observations up to the scale of the Solar System, but what if the theory is insufficient on cosmological scales, beyond the size of individual galaxies? The creativity of researchers has led to several modified models of gravity. The simplest ones introduce a new element, a “scalar field”, which changes the way space and time are distorted by a mass, making the gravitational potentials deeper or shallower. A brilliant physicist named Gregory Horndeski has developed the most general theory of gravity involving a scalar field, which has become a key paradigm. 

 

How can we assess whether the Horndeski theory provides a better description of the Universe than General Relativity? The two theories predict different relations between the mass of an object and the resulting gravitational potential. This will affect the predicted motions of galaxies in their local environments, which in Horndeski gravity are faster or slower than in General Relativity. Current measurements of these motions are not sufficiently precise to discriminate between the two theories, but cosmologists are expecting to achieve this with upcoming galaxy surveys. 

 

However, instead of pausing our stroll while waiting for new data, one more element must be taken into account. The cosmic cocktail described by the standard cosmological model contains another obscure ingredient, dark matter, which does not emit light and accounts for around 80% of the matter in the Universe. Physicists have observed its gravitational impact on galaxies, but its properties remain mysterious. On very large scales, it could be that dark matter falls into the gravitational potentials in a different way from ordinary matter, and this possibility was recently included in an extension of the Horndeski theory. 

 

This extension introduces a complication: in a recent study, we have shown that this allows for compensating effects in the motions of galaxies. For example, we could live in a Horndeski universe where the gravitational potentials are shallower than in General Relativity, leading to slower galactic motions. However, this effect could be compensated by changing the impact of gravity on the dark matter contained in the galaxies, such that their motion would be exactly the same as in General Relativity. This would make the two theories completely indistinguishable. 

 

Luckily, we have identified a new method to settle the dispute. The key ingredient is the fact that time gets distorted in the presence of a gravitational potential, flowing more slowly at the bottom of the potential than outside of it. This effect can be measured from a frequency change in the light emitted by galaxies, which can be compared with the observed galactic motions. The relation between these two measurements is different in the two theories of gravity, providing a clear way to distinguish between them. 

 

The distortion of time is a tiny effect, but is forecasted to be measurable by future missions like the Square Kilometre Array Phase 2 planned for the early 2030s. We have demonstrated that such future measurements might yield evidence in favor of Horndeski gravity or set constraints on the largest allowed deviations from General Relativity. This will be one step forward towards understanding the fundamental properties of gravity, in the quest to shed light on the accelerated cosmic expansion.



Study funded by Prof. Bonvin's ERC consolidator grant - full details: European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 863929; project title “Testing the law of gravity with novel large-scale structure observables”).