Galileon gravity and its relevance to late time cosmic acceleration

TL;DR

The paper investigates covariant galileon gravity as an infrared modification of gravity to explain late-time cosmic acceleration, focusing on L3–L4 (and briefly L5) terms and their cosmological implications. It demonstrates that a stable self-accelerating solution generally does not exist at third order, but emerges with fourth-order Galileon terms under specific positivity conditions on the couplings, and it analyzes both homogeneous FRW dynamics and a spherically symmetric screening scenario via the Vainshtein mechanism. The work also examines the causal structure and stability of perturbations, including a Vainshtein-screened static solution that can exhibit superluminal propagation without closed causal curves, and derives the modified growth equation with an effective gravitational coupling $G_{\rm eff}$ for matter perturbations. These results illuminate how Galileon fields can drive acceleration while remaining compatible with local gravity tests, and they point to distinct growth-of-structure signatures that could distinguish Galileon gravity from $\Lambda$CDM in observations.

Abstract

We consider the covariant galileon gravity taking into account the third order and fourth order scalar field Lagrangians L_3(π) and L_4(π) consisting of three and four $π$'s with four and five derivatives acting on them respectively. The background dynamical equations are set up for the system under consideration and the stability of the self accelerating solution is demonstrated in general setting. We extended this study to the general case of the fifth order theory. For spherically symmetric static background, we spell out conditions for suppression of fifth force effects mediated by the galileon field $π$. We study the field perturbations in the fixed background and investigate conditions for their causal propagation. We also briefly discuss metric fluctuations and derive evolution equation for matter perturbations in galileon gravity.