Growth index of matter perturbations in running vacuum models

TL;DR

This paper derives the growth index of matter perturbations in flat cosmological models with a running vacuum energy depending on redshift, extending the standard $ ext{Lambda}$CDM model to include mild dynamical effects.

Contribution

It provides the first derivation of the growth index for running vacuum models with a specific H^2 dependence, expanding the analytical understanding of structure growth in these models.

Findings

The growth index for the model is approximately (6+3ν)/(11-12ν).

The derived growth index smoothly extends the standard $ ext{Lambda}$CDM result of 6/11.

The model predicts a mild dynamical effect on cosmological observables.

Abstract

We derive for the first time the growth index of matter perturbations of the FLRW flat cosmological models in which the vacuum energy depends on redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which apart from a leading constant term $\Lambda_0$ there is also a $H^{2}$-dependence in the functional form of vacuum, namely $\Lambda(H)=\Lambda_{0}+3\nu (H^{2}-H^{2}_{0})$. Since $|\nu|\ll1$ this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at the perturbation level we find that the growth index of the running vacuum cosmological model is $\gamma_{\Lambda_{H}} \approx \frac{6+3\nu}{11-12\nu}$ and thus it nicely extends analytically the result of the $\Lambda$CDM model, $\gamma_{\Lambda}\approx 6/11$.