Cosmological scalar perturbations in Horndeski-like gravity

TL;DR

This paper investigates the stability and entropy bounds of scalar perturbations in Horndeski-like gravity, a scalar-tensor theory inspired by string theory, and compares scalar and tensor sector behaviors.

Contribution

It provides a stability analysis of the scalar sector in Horndeski-like gravity and explores entropy bounds related to particle production and horizon entropy.

Findings

Scalar sector stability conditions identified

Entropy bounds related to particle production and horizons analyzed

Comparison of scalar and tensor sector stability and entropy properties

Abstract

Scalar-tensor theories are promising dark energy models. A promising scalar-tensor theory, called Horndeski-like gravity, is coming from the application of the Horndeski gravity in string theory and cosmology that takes into account two dilaton fields. In this work we study the stability of the scalar sector of this theory and compare it with that coming from the previously studied tensor sector. With the first-order formalism we investigate the allowed background solutions. Focusing on the background solution with a single scalar field, the entropy coming from particle production $S_{in}$ and that of the apparent horizon $S$ will be studied, which translates into \textit{entropy bounds}. These entropy bounds are compared with the stability of the scalar and tensor sector as well. The gravitational slip (minus one) to entropy ratio is also considered as a possible replacement for the usual shear viscosity to entropy ratio for black holes.