Cosmological perturbations in $k$-essence model

TL;DR

This paper investigates the limitations of the subhorizon approximation in $k$-essence cosmological models and highlights how the sound speed significantly affects matter perturbation evolution, with implications for future observations distinguishing it from $$Lambda$CDM.

Contribution

It demonstrates that the subhorizon approximation may not be valid in $k$-essence models and analyzes the impact of sound speed on matter perturbations.

Findings

Subhorizon approximation is not always valid in $k$-essence models.

Sound speed influences the evolution of matter density perturbations.

Future observations could differentiate $k$-essence from $$Lambda$CDM.

Abstract

Subhorizon approximation is often used in cosmological perturbation theory. In this paper, however, it is shown that the subhorizon approximation is not always a good approximation at least in case of $k$-essence model. We also show that the sound speed given by $k$-essence model exerts a huge influence on the time evolution of the matter density perturbation, and the future observations could clarify the differences between the $\Lambda$CDM model and $k$-essence model.