# Matter growth in extended $\Lambda$CDM cosmology

## TL;DR

This paper extends the standard $ ext{Lambda}$CDM cosmology by incorporating scalar-tensor modifications, anisotropic stresses, and dark-energy perturbations to analyze their effects on matter growth and compare with observational data.

## Contribution

It develops an effective fluid approach for matter growth in an extended $ ext{Lambda}$CDM model including anisotropic stresses and dark-energy perturbations, with explicit background dynamics.

## Key findings

- Deviations from standard background affect matter growth rate.
- Anisotropic stresses influence the growth function $f \sigma_8$.
- Model results are compared with recent RSD measurements.

## Abstract

On the basis of a previously established scalar-tensor extension of the $\Lambda$CDM model we develop an effective fluid approach for the matter growth function. This extended $\Lambda$CDM (henceforth $e_{\Phi}\Lambda$CDM) cosmology takes into account deviations from the standard model both via a modified background expansion and by the inclusion of geometric anisotropic stresses as well as of perturbations of the geometric dark-energy equivalent. The background dynamics is governed by an explicit analytic expression for the Hubble rate in which modifications of the standard model are given in terms of a single constant parameter [1]. To close the system of fluid-dynamical perturbation equations we introduce two phenomenological parameters through which the anisotropic stress is related both to the total energy density perturbation of the cosmic substratum and to relative perturbations in the effective two-component system. We quantify the impact of deviations from the standard background, of anisotropic stresses and of non-vanishing perturbations of the effective dark-energy component on the matter growth rate function $f \sigma_8$ and confront the results with recent redshift-space distortion (RSD) measurements.