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

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.