Cosmology of the Galileon from Massive Gravity

TL;DR

The paper develops a covariant proxy for the decoupling-limit of ghost-free massive gravity to study cosmology without solving the full non-linear theory. By covariantizing Galileon-like interactions, it demonstrates a stable self-accelerating de Sitter solution with $H^2\sim m^2$ and shows the helicity-0 mode enhances structure growth relative to LCDM, while degravitating solutions are not realized in this proxy. It analyzes perturbations, derives a modified growth equation, and compares covariantizations from the Jordan and Einstein frames, finding consistency in the regime studied. These results offer testable predictions for large-scale structure and lensing, and highlight the role of the Vainshtein mechanism in massive gravity-inspired cosmologies.

Abstract

We covariantize the decoupling limit of massive gravity proposed in arXiv:1011.1232 and study the cosmology of this theory as a proxy, which embodies key features of the fully non-linear covariant theory. We first confirm that it exhibits a self-accelerating solution, similar to what has been found in arXiv:1010.1780, where the Hubble parameter corresponds to the graviton mass. For a certain range of parameters fluctuations relative to the self-accelerating background are stable and form an attractor solution. We also show that a degravitating solution can not be constructed in this covariantized proxy theory in a meaningful way. As for cosmic structure formation, we find that the helicity-0 mode of the graviton causes an enhancement relative to LCDM. For consistency we also compare proxy theories obtained starting from different frames in the decoupling limit and discuss the possibility of obtaining a non-representative proxy theory by choosing the wrong starting frame.

Figures (1)

• Figure 1: Fluid densities $\rho^{rad}\sim a^{-4}$, $\rho^{mat}\sim a^{-3}$ and $\rho_\pi$ during the epochs of radiation, matter and $\Lambda$-domination normalised to today $\rho_\pi$. During the radiation domination the energy density for $\pi$ goes as $\rho^\pi_{\rm rad}\sim a^{-1/2}$ and during matter dominations as $\rho^\pi_{\rm mat}\sim a^{-3/2}$ and is constant for later times $\rho^\pi_\Lambda={\rm const}$.