Revisiting scalar and tensor perturbations in a nonlocal gravity

TL;DR

This paper investigates the impact of a nonzero auxiliary field in nonlocal RT gravity on cosmic evolution and gravitational wave signals, revealing negligible effects on background evolution but potential observable influences on gravitational wave amplitudes.

Contribution

It demonstrates that the background auxiliary field $S_i$ grows with the universe's expansion and assesses its effects on cosmic and gravitational wave observations, providing new insights into nonlocal gravity.

Findings

Background $S_i$ is proportional to $a^2$ with universe expansion.

Cosmic background evolution is unaffected by $S_i$.

Nonzero $S_i$ influences gravitational wave amplitude and luminosity distance.

Abstract

Nonlocal RT gravity is a successful modified gravity theory, which not only explains the late-time cosmic acceleration but also behaves well in the solar system. Previous analysis generally assumes the auxiliary field $S_i$ vanishes at the cosmic background. However, we find the background $S_i$ is proportional to $a^2$ with the expansion of the universe. Then we discuss the influence of the nonzero background $S_i$ on the cosmic background evolution, the scalar and tensor perturbations. We find the cosmic background evolution is independent of $S_i$, and the influence of the nonzero background $S_i$ on the weak field limit at solar system scales is negligible. For the tensor perturbation, we find the only possible observable effect is the influence of nonzero background $S_i$ on the LIGO gravitational wave amplitude and also luminosity distance. Future high redshift gravitational wave observations could be used to constrain the background value of $S_i$.