Testing for dynamical dark energy models with redshift-space distortions

TL;DR

This paper derives an analytic formula for the growth rate of matter perturbations in dynamical dark energy models using redshift-space distortions, and applies it to constrain such models with observational data.

Contribution

It provides a new analytic expression for f(z) sigma_8(z) applicable to various dark energy models under specific conditions.

Findings

Derived a convenient analytic formula for growth rate in dynamical dark energy models.

Placed observational constraints on constant w and tracking quintessence models.

Applicable to models with nearly constant w and sound speed close to 1.

Abstract

The red-shift space distortions in the galaxy power spectrum can be used to measure the growth rate of matter density perturbations delta_m. For dynamical dark energy models in General Relativity we provide a convenient analytic formula of f(z) sigma_8(z) written as a function of the redshift z, where f=d ln delta_m/d ln a (a is the cosmological scale factor) and sigma_8 is the rms amplitude of over-density at the scale 8 h^{-1} Mpc. Our formula can be applied to the models of imperfect fluids, quintessence, and k-essence, provided that the dark energy equation of state w does not vary significantly and that the sound speed is not much smaller than 1. We also place observational constraints on dark energy models of constant w and tracking quintessence from the recent data of red-shift space distortions.