Evolution of sub-horizon cold dark matter perturbations

TL;DR

This paper derives a generalized equation to describe how cold dark matter perturbations evolve on sub-horizon scales during dark energy domination, enhancing understanding of structure formation in the universe.

Contribution

The paper introduces the $w$-Meszaros equation, extending previous models to arbitrary dark energy equations of state, and provides analytical solutions for dark matter perturbation evolution.

Findings

Analytical solutions for cold dark matter perturbations during dark energy domination.

Generalization of the Meszaros equation to arbitrary equation of state parameter.

Qualitative understanding of perturbation evolution without dark energy perturbations.

Abstract

We investigate the evolution of sub-horizon cold dark matter perturbation in the dark energy dominated era of the Universe. By generalising the Meszaros equation to be valid for an arbitrary equation of state parameter, we derive the $w$-Meszaros equation. Its solutions determine the evolution of the cold dark matter perturbation by neglecting dark energy perturbations. Our analytical results provide a qualitative understanding of this evolution.