[Paper Review] Evolution of sub-horizon cold dark matter perturbations

Christian G. Bohmerand, Gabriela Caldera-Cabral|arXiv (Cornell University)|Aug 17, 2010

Cosmology and Gravitation Theories6 references3 citations

TL;DR

This paper generalizes the Meszaros equation to derive the $w$-Meszaros equation, which models the evolution of sub-horizon cold dark matter perturbations in a dark energy-dominated universe with an arbitrary equation of state parameter $w$. The analytical solutions reveal how dark energy's equation of state influences the growth of cold dark matter structures, offering a qualitative framework for understanding structure formation in late-time cosmology.

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.

Motivation & Objective

• To understand the evolution of sub-horizon cold dark matter perturbations during the dark energy-dominated era of the Universe.
• To generalize the standard Meszaros equation to accommodate an arbitrary dark energy equation of state parameter $w$.
• To provide an analytical framework for studying cold dark matter growth without including dark energy perturbations.

Proposed method

• Derive the $w$-Meszaros equation by extending the standard Meszaros equation to include an arbitrary equation of state parameter $w$ for dark energy.
• Solve the $w$-Meszaros equation analytically to determine the time evolution of cold dark matter perturbations.
• Neglect perturbations in the dark energy component to isolate the effect of $w$ on cold dark matter growth.
• Use the derived solutions to analyze the qualitative behavior of cold dark matter perturbations across different values of $w$.
• Apply standard cosmological perturbation theory techniques within the linear regime to model sub-horizon scales.

Experimental results

Research questions

• RQ1 How does the equation of state parameter $w$ of dark energy influence the growth of cold dark matter perturbations in the sub-horizon regime?
• RQ2 What is the form of the generalized Meszaros equation when dark energy has an arbitrary $w$?
• RQ3 How does the growth rate of cold dark matter structures change in the dark energy-dominated era compared to the matter-dominated era?
• RQ4 What analytical solutions emerge from the $w$-Meszaros equation for different values of $w$?
• RQ5 How does the neglect of dark energy perturbations affect the validity and interpretation of the cold dark matter perturbation evolution?

Key findings

• The $w$-Meszaros equation is successfully derived as a generalization of the standard Meszaros equation for arbitrary $w$, enabling the study of cold dark matter perturbations in a dark energy-dominated universe.
• Analytical solutions to the $w$-Meszaros equation reveal that the growth of cold dark matter perturbations depends on the value of $w$, with distinct behaviors for $w = -1$ and $w \neq -1$.
• The solutions provide a qualitative understanding of how the equation of state of dark energy modulates the growth rate of cold dark matter structures on sub-horizon scales.
• The neglect of dark energy perturbations allows for a simplified yet insightful analysis of cold dark matter evolution, isolating the effect of $w$ on structure formation.
• The derived framework offers a theoretical basis for interpreting future observations of large-scale structure in the context of varying dark energy models.