Scalar Field Dark Energy Perturbations and their Scale Dependence

TL;DR

This paper investigates how dark energy perturbations vary across different scales in a quintessence model, highlighting their negligible impact on small scales but significant influence on large scales, aiding in distinguishing dark energy models.

Contribution

It provides a scale-dependent analysis of dark energy perturbations in a quintessence model, emphasizing their importance on large scales for model discrimination.

Findings

Dark energy perturbations are negligible below the Hubble radius.

Large scale dark energy perturbations affect matter power spectrum.

Large scale matter power spectrum is suppressed compared to $\\Lambda$CDM.

Abstract

We estimate the amplitude of perturbation in dark energy at different length scales for a quintessence model with an exponential potential. It is shown that on length scales much smaller than hubble radius, perturbation in dark energy is negligible in comparison to that in in dark matter. However, on scales comparable to the hubble radius ($\lambda_{p}>1000\mathrm{Mpc}$) the perturbation in dark energy in general cannot be neglected. As compared to the $\Lambda$CDM model, large scale matter power spectrum is suppressed in a generic quintessence dark energy model. We show that on scales $\lambda_{p} < 1000\mathrm{Mpc}$, this suppression is primarily due to different background evolution compared to $\Lambda$CDM model. However, on much larger scales perturbation in dark energy can effect matter power spectrum significantly. Hence this analysis can act as a discriminator between $\Lambda$CDM model and other generic dark energy models with $w_{de} \neq -1$.