Testing ΛCDM with the growth function δ(a):: Current constraints

We have compiled a data set consisting of 22 data points at a redshift range (0.15, 3.8) which can be used to constrain the linear perturbation growth rate f= dln delta n/dlna. 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 data points constrain f indirectly through the rms mass fluctuation sigma(8)(z) inferred from L-y-alpha at various redshifts. Our analysis tests the consistency of the Lambda CDM model and leads to a constraint of the Wang-Steinhardt growth index gamma [defined from f = Omega(m)(a)(gamma)] as gamma=0.67(-0.17)(+0.20). This result is clearly consistent at 1 sigma with the value gamma = 6/11 = 0.545 predicted by Lambda CDM. We also apply our analysis on a new null test of Lambda CDM 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 Lambda CDM provides an excellent fit to the current linear growth data.