Quasi-Dilaton: Theory and Cosmology

TL;DR

The paper extends ghost-free massive gravity by a quasi-dilaton scalar $\sigma$ and a new global symmetry $\sigma \to \sigma - \alpha M_{\rm Pl},\; \phi^a \to e^{\alpha}\phi^a$, yielding quasi-dilaton massive gravity (QMG). It demonstrates ghost-freedom via the decoupling limit where the $\pi$ (helicity-0) and $\sigma$ interactions form a bi-Galileon system with enhanced shift symmetry, and argues that full-theory constraints preserve this property. The model retains the Vainshtein mechanism, ensuring recovery of GR near sources, and uniquely permits flat FRW cosmology with self-accelerated de Sitter branches for a broad parameter range, unlike standard massive GR. Perturbations around these cosmological backgrounds generally involve two scalar degrees of freedom with no BD ghost, and the theory predicts a modified expansion history via different effective Newton constants, which could be probed observationally. The work highlights potential degravitating solutions and outlines directions for deeper phenomenological analysis and stability studies.

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.