Testing LCDM with the Growth Function \delta(a): Current Constraints

TL;DR

This paper compiles growth rate data to test the LCDM model, constrains the growth index gamma, and confirms LCDM's consistency with current linear growth observations.

Contribution

It provides new constraints on the growth index gamma using an expanded dataset and introduces a null test of LCDM that avoids derivatives of H(z).

Findings

Gamma constrained to 0.67^{+0.20}_{-0.17}

Results consistent with LCDM prediction gamma=0.55

LCDM fits current growth data well

Abstract

We have compiled a dataset consisting of 22 datapoints at a redshift range (0.15,3.8) which can be used to constrain the linear perturbation growth rate f=\frac{d\ln\delta}{d\ln a}. Five of these data-points constrain directly the growth rate f through either redshift distortions or change of the power spectrum with redshift. The rest of the datapoints constrain f indirectly through the rms mass fluctuation \sigma_8(z) inferred from Ly-\alpha at various redshifts. Our analysis tests the consistency of the LCDM model and leads to a constraint of the Wang-Steinhardt growth index \gamma (defined from f=\Omega_m^\gamma) as \gamma=0.67^{+0.20}_{-0.17}. This result is clearly consistent at $1\sigma$ with the value \gamma={6/11}=0.55 predicted by LCDM. A first order expansion of the index \gamma in redshift space leads to similar results.We also apply our analysis on a new null test of LCDM which is similar to the one recently proposed by Chiba and Nakamura (arXiv:0708.3877) but does not involve derivatives of the expansion rate $H(z)$. This also leads to the fact that LCDM provides an excellent fit to the current linear growth data.