A systematic approach to generalisations of General Relativity and their cosmological implications

TL;DR

This paper reviews recent theoretical developments in generalized gravity theories beyond Einstein's General Relativity, exploring their formulations, motivations, and empirical viability in addressing modern cosmological and particle physics challenges.

Contribution

It systematically surveys various extended gravity theories, including scalar, vector, and tensor modifications, highlighting their construction, differences, and potential to explain cosmological phenomena.

Findings

Constructed consistent field theories with additional degrees of freedom.

Analyzed empirical viability of generalized gravity models.

Compared different formulations and their cosmological implications.

Abstract

A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime. Even though Einstein's interpretation of gravity in terms of the curvature of spacetime is commonly adopted, the assignment of geometrical concepts to gravity is ambiguous because General Relativity allows three entirely different, but equivalent approaches of which Einstein's interpretation is only one. From a field-theoretical perspective, however, the construction of a consistent theory for a Lorentz-invariant massless spin-2 particle uniquely leads to General Relativity. Keeping Lorentz invariance then implies that any modification of General Relativity will inevitably introduce additional propagating degrees of freedom into the gravity sector. Adopting this perspective, we will review the recent progress in constructing consistent field theories of gravity based on additional scalar, vector and tensor fields. Within this conceptual framework, we will discuss theories with Galileons, with Lagrange densities as constructed by Horndeski and beyond, extended to DHOST interactions, or containing generalized Proca fields and extensions thereof, or several Proca fields, as well as bigravity theories and scalar-vector-tensor theories. We will review the motivation of their inception, different formulations, and essential results obtained within these classes of theories together with their empirical viability.