Cosmology in gravity models with broken diffeomorphisms

TL;DR

This paper explores gravity models that break diffeomorphism invariance to transverse diffeomorphisms, revealing rich cosmological behaviors including standard $ ext{Lambda}$CDM and alternative dark energy dynamics, with potential for universe recollapse.

Contribution

It identifies stable TDiff gravity models with an extra scalar graviton that match local tests and exhibit diverse cosmological evolutions, extending beyond general relativity.

Findings

Standard $ ext{Lambda}$CDM as a special case when the scalar mode is inactive.

The extra scalar contribution can mimic dark energy or track background matter.

Solutions with universe recollapse are possible depending on initial conditions.

Abstract

We study the cosmological implications of gravity models which break diffeomorphisms (Diff) invariance down to transverse diffeomorphisms (TDiff). We start from the most general gravitational action involving up to quadratic terms in derivatives of the metric tensor and identify TDiff models as the only stable theories consistent with local gravity tests. These models propagate an additional scalar graviton and although they are indistinguishable from GR at the post-Newtonian level, their cosmological dynamics exhibits a rich phenomenology. Thus we show that the model includes standard $\Lambda$CDM as a solution when the extra scalar mode is not excited, but different cosmological evolutions driven by the new term are possible. In particular, we show that for a soft Diff breaking, the new contribution always behaves as a cosmological constant at late times. When the extra contribution is not negligible, generically its evolution either behaves as dark energy or tracks the dominant background component. Depending on the initial conditions, solutions in which the universe evolves from an expanding to a contracting phase, eventually recollapsing are also possible.