Growth of matter perturbations in clustered holographic dark energy cosmologies

TL;DR

This paper analyzes how matter fluctuations grow in holographic dark energy cosmologies, deriving new analytical expressions for the growth index and comparing them with standard cosmology using observational data.

Contribution

It introduces a new analytical method to derive the growth index of matter perturbations in holographic dark energy models, including clustering effects, and compares these with the standard Λ cosmology.

Findings

Growth index for homogeneous holographic dark energy is approximately 4/7.

Clustering in holographic dark energy models modifies the growth index based on effective sound speed.

The growth index is about 4.8% larger than in the Λ cosmology.

Abstract

We investigate the growth of matter fluctuations in holographic dark energy cosmologies. First we use an overall statistical analysis involving the latest observational data in order to place constraints on the cosmological parameters. Then we test the range of validity of the holographic dark energy models at the perturbation level and its variants from the concordance $\Lambda$ cosmology. Specifically, we provide a new analytical approach in order to derive, for the first time, the growth index of matter perturbations. Considering a homogeneous holographic dark energy we find that the growth index is $\gamma \approx \frac{4}{7}$ which is somewhat larger ($\sim 4.8\%$) than that of the usual $\Lambda$ cosmology, $\gamma^{(\Lambda)}\approx \frac{6}{11}$. Finally, if we allow clustering in the holographic dark energy models then the asymptotic value of the growth index is given in terms of the effective sound speed $c_{\rm eff}^2$, namely $\gamma \approx \frac{3(1-c_{\rm eff}^2)}{7}$.