Cosmic Acceleration and the Helicity-0 Graviton

TL;DR

This work analyzes cosmology in the decoupling limit of a ghost-free nonlinear covariant extension of Fierz-Pauli massive gravity, revealing a self-accelerated solution with $H^2 \sim m^2$ driven by a helicity-0 condensate whose stress tensor yields a ΛCDM-like background. Crucially, fluctuations around this background can be stable, and the helicity-0 mode can decouple from arbitrary sources at linear order, reproducing GR predictions at sub-horizon scales. The authors also investigate degravitation, showing that the theory can scherm a large cosmological constant in the decoupling limit via a degravitating branch and a de Sitter branch, but fifth-force constraints severely limit the allowed degravitated CC, challenging the viability of solving the old cosmological constant problem within this framework. They further analyze the ghostless theory in the Einstein frame, demonstrating parameter-dependent routes to diagonalizable actions and highlighting the phenomenological implications, including horizon-scale deviations and the need for a full nonperturbative treatment to assess viability. Overall, the paper provides concrete mechanisms for self-acceleration and degravitation within a controlled limit of massive gravity, while identifying significant obstacles for addressing the cosmological constant problem in this setup.

Abstract

We explore cosmology in the decoupling limit of a non-linear covariant extension of Fierz-Pauli massive gravity obtained recently in arXiv:1007.0443. In this limit the theory is a scalar-tensor model of a unique form defined by symmetries. We find that it admits a self-accelerated solution, with the Hubble parameter set by the graviton mass. The negative pressure causing the acceleration is due to a condensate of the helicity-0 component of the massive graviton, and the background evolution, in the approximation used, is indistinguishable from the ΛCDM model. Fluctuations about the self-accelerated background are stable for a certain range of parameters involved. Most surprisingly, the fluctuation of the helicity-0 field above its background decouples from an arbitrary source in the linearized theory. We also show how massive gravity can remarkably screen an arbitrarily large cosmological constant in the decoupling limit, while evading issues with ghosts. The obtained static solution is stable against small perturbations, suggesting that the degravitation of the vacuum energy is possible in the full theory. Interestingly, however, this mechanism postpones the Vainshtein effect to shorter distance scales. Hence, fifth force measurements severely constrain the value of the cosmological constant that can be neutralized, making this scheme phenomenologically not viable for solving the old cosmological constant problem. We briefly speculate on a possible way out of this issue.