A non-local origin for massive gravity and late-time acceleration

TL;DR

This paper proposes a non-local gravity model that naturally produces a massive graviton and explains late-time cosmic acceleration, while remaining free of ghosts and consistent with observations.

Contribution

It introduces a novel non-local gravity action that yields a stable de Sitter universe and a ghost-free massive graviton, offering an alternative to scalar-tensor dark energy models.

Findings

The model has a stable de Sitter attractor.

All perturbations are ghost-free and stable.

Predicts distinct gravitational wave polarization signatures.

Abstract

The accelerated expansion of the universe poses a significant challenge to General Relativity. Non-local modifications to gravity have emerged as a compelling class of theories to address this dark energy puzzle. Building upon earlier proposals, we investigate a specific non-local modified gravity action incorporating terms like $R\Box^{-2}R$, $R^{\mu\nu}\Box^{-2}R_{\mu\nu}$, $R^{\mu\nu\sigma\delta}\Box^{-2}R_{\mu\nu\sigma\delta}$ and demonstrate that it provides a dynamical origin for a massive graviton by reducing to the standard and extended Fierz-Pauli action at the linearized level. A fixed-point analysis of the background cosmology reveals a stable de Sitter attractor, ensuring the model naturally drives accelerated expansion. Crucially, we investigate the cosmological perturbations and show that the theory's six propagating degrees of freedom are free from ghost instabilities. We further demonstrate that all large-scale tensor modes are dynamically stable and decay on the accelerating background. This ghost-free massive gravity extension provides distinct predictions for gravitational wave polarizations and is theoretically consistent with $\mathbf{\Lambda CDM}$ at late times, positioning it as a unique alternative to scalar-tensor models like $f(R)$ and Galileons. This robust stability at both the background and perturbative levels establishes our model as a consistent and compelling alternative to the standard $\Lambda$CDM paradigm.