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

TL;DR

This paper addresses cosmic acceleration by developing a non-local modification of gravity with terms $R\,\Box^{-2}R$, $R^{\mu\nu}\,\Box^{-2}}R_{\mu\nu}$ and $R^{\mu\nu\rho\sigma}\,\Box^{-2}}R_{\mu\nu\rho\sigma}$. By localizing the action with auxiliary fields, it maps to (extended) Fierz-Pauli (FP) massive gravity in the linear limit and demonstrates a ghost-free six DOF spectrum. A dynamical systems analysis reveals a robust de Sitter attractor at late times, yielding natural acceleration without a cosmological constant. The study further shows stability of cosmological perturbations on the de Sitter background and discusses observational implications, including distinctive gravitational-wave polarizations, while ensuring consistency with $\mathbf{\Lambda CDM}$ at late times. This framework provides a theoretically consistent IR modification of gravity with potentially testable cosmological and GW 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 $R\Box^{-2}R$, $R^{μν}\Box^{-2}R_{μν}$, $R^{μνσδ}\Box^{-2}R_{μνσδ}$ 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 $\mathbf{ΛCDM}$ 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 $Λ$CDM paradigm.

Figures (2)

• Figure 1: Directional flow in the density parameter space with four initial configurations and their fixed point analysis. The above plots show universality of deSitter attractor in our non-local model with mass parameter $m$ being arbitrary and it is absorbed in the density parameters. Here directional flow is plotted in $\Omega_{m}-\Omega_{DE}$ plane and the physical configurations are located in $\Omega_{m} + \Omega_{DE} = 1$ line with $\Omega_{m}$ and $\Omega_{DE}$ lie between $0$ and $1$.
• Figure 2: Directional flow in the density parameter space when both $\mu_{1}, \mu_{2} \neq 0$, related to mass parameter $m$ and the fixed point analysis. Like earlier, here directional flow is also plotted in $\Omega_{m}-\Omega_{DE}$ plane and the physical configurations are located in $\Omega_{m} + \Omega_{DE} = 1$ line with $\Omega_{m}$ and $\Omega_{DE}$ lie between $0$ and $1$.