Vainshtein Mechanism in Generalised Massive Gravity

TL;DR

This paper investigates the Vainshtein screening mechanism in a generalized massive gravity theory, demonstrating stable cosmological solutions, unique scalar graviton dynamics, and consistency with solar system tests.

Contribution

It provides a non-linear analysis of perturbations in a Lorentz-invariant massive gravity extension, revealing new scalar solutions and confirming the Vainshtein mechanism's effectiveness.

Findings

Identifies a distinct scalar graviton equation from other theories.

Finds a new nonlinear scalar mode solution.

Shows the PPN parameter approaches GR value at solar system scales.

Abstract

We present a non-linear analysis of perturbations around cosmological solutions in Generalised Massive gravity. This Lorentz invariant theory is an extension of de Rham, Gabadadze, Tolley massive gravity that propagates $5$ degrees of freedom while allowing stable open FLRW cosmologies. For a minimal model that supports a self-accelerating background, we study the dynamics of non-linear perturbations. We find that the equation for the scalar graviton is distinct from the analogues in Horndeski and DHOST theories. We numerically solve the equation to find a new type of nonlinear solution for the scalar mode, and confirm the presence of a Vainshtein screening mechanism. We show that the PPN parameter approaches its GR value at solar system scales and satisfies the current bounds.