Quasi-Dilaton: Theory and Cosmology

TL;DR

This paper introduces a quasi-dilaton extension to massive gravity, maintaining theoretical consistency, enabling flat FRW solutions, and offering testable cosmological predictions distinct from standard massive GR.

Contribution

It proposes a new quasi-dilaton field in massive gravity that preserves symmetry, allows flat FRW solutions, and provides novel cosmological implications.

Findings

The theory remains consistent with observations and theoretical constraints.

It retains the Vainshtein mechanism for screening.

It predicts self-accelerated cosmological solutions with testable differences from standard models.

Abstract

General Relativity (GR), with or without matter fields, admits a natural extension to a scale invariant theory that requires a dilaton. Here we show that the recently formulated massive GR, minimally coupled to matter, possesses a new global symmetry related to scaling of the reference coordinates w.r.t. the physical ones. The field enforcing this symmetry, dubbed here quasi-dilaton, coincides with an ordinary dilaton if only pure gravity is considered, but differs from it when the matter Lagrangian is present. We study: (1) Theoretical consistency of massive GR with the quasi-dilaton; (2) Consistency with observations for spherically symmetric sources on (nearly) flat backgrounds; (3) Cosmological implications of this theory. We find that: (I) The theory with the quasi-dilaton is as consistent as massive GR is. (II) The Vainshtein mechanism is generically retained, owing to the fact that in the decoupling limit there is an enhanced symmetry, which turns the quasi-dilaton into a second galileon, consistently coupled to a tensor field. (III) Unlike in massive GR, there exist flat FRW solutions. In particular, we find self-accelerated solutions and discuss their quadratic perturbations. These solutions are testable by virtue of the different effective Newton's constants that govern the Hubble expansion and structure growth.