Cosmological modifications of gravity as relativistic media

For twenty five years, we have known that the expansion of the universe is accelerating. This requires that the majority of the energy of the universe is currently in some form of matter with negative pressure – vacuum energy according to the ΛCDM model of cosmology. Could it be something else? The latest measurements by observatories such as DESI [1] are pointing toward a non-trivial behaviour of this accelerating component.

One of the candidates for dark energy is a modification of gravity, a deviation from General Relativity. On the largest – super-galactic – scales gravity is not yet well constrained, so General Relativity might not be a good description of the dynamics there. On the other hand, in the solar system, gravity is well understood. Modified gravity theories have inbuilt non-linearities called screening mechanisms which can suppress new physics and return the phenomenology to the standard one close to stars. However, this screening works well for slow-moving sources, while the behaviour of relativistic bodies such as black holes and neutron stars in these theories is less understood [2]. The detection of gravitational waves from relativistic systems such a inspiralling binary black holes has opened up a new and much more direct method of testing the nature of gravity [3].

This project is aimed at trying to understand the physics of general gravity theories by exploiting the language of the theory of media [4]: we can think of the emitting source and the spacetime between it and the detectors as a medium through which small fluctutations – gravitational waves – propagate. This medium can be described using an effective – acoustic – metric encoding, for example, the index of refraction. A theory of non-linear gravitational waves in vacuum can apparently be described as a theory of linear waves in a different effective spacetime.

This project is best suited for a student with a preference for theoretical approaches.

References:

[1] DESI collaboration, DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
[2] Babichev, Esposito-Ferèse, Sawicki and Trombetta: Large black-hole scalar charges induced by cosmology in Horndeski theories
[3] Perkins, Yunes and Berti: Probing Fundamental Physics with Gravitational Waves: The Next Generation
[4] Sawicki, Trenkler and Vikman: Causality and stability from acoustic geometry