Cosmological perturbations in mimetic Horndeski gravity

TL;DR

This paper analyzes linear scalar perturbations in mimetic Horndeski gravity, revealing zero sound speed and constant comoving curvature perturbation, indicating no wave-like scalar degrees of freedom.

Contribution

It demonstrates that scalar perturbations in mimetic Horndeski gravity have zero sound speed and provides solutions for potential evolution, advancing understanding of perturbation dynamics in this theory.

Findings

Scalar perturbations have zero sound speed.

Comoving curvature perturbation remains constant.

No wave-like scalar degrees of freedom exist.

Abstract

We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic $G^3$ theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.