Observational constraints on the linear fluctuation growth rate

TL;DR

This paper introduces a simple, generalized fitting formula for the linear growth rate of matter perturbations, useful for testing dark energy models with upcoming experiments, and constrains its parameters using galaxy and Lyman-alpha data.

Contribution

It proposes a new, simple parametrization of the linear growth rate that encompasses models with faster growth than standard, and provides observational constraints on its parameters.

Findings

The growth rate index γ is constrained to 0.6_{-0.3}^{+0.4}.

The additional growth parameter η is constrained to 0.0_{-0.2}^{+0.3}.

The proposed formula accurately reproduces growth functions in various models.

Abstract

Several experiments in the near future will test dark energy through its effects on the linear growth of matter perturbations. It is therefore important to find simple and at the same time general parametrizations of the linear growth rate. We show that a simple fitting formula that generalizes previous expressions reproduces the growth function in models that allow for a growth faster than standard, as for instance in scalar-tensor models. We use data from galaxy and Lyman-$\alpha$ power spectra to constrain the linear growth rate. We find $\gamma=0.6_{-0.3}^{+0.4}$ for the growth rate index and $\eta=0.0_{-0.2}^{+0.3}$ for the additional growth parameter we introduce.