Testing LCDM with the Growth Function δ(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\lnδ}{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 σ_8(z) inferred from Ly-αat various redshifts. Our analysis tests the consistency of the LCDM model and leads to a constraint of the Wang-Steinhardt growth index γ(defined from f=Ω_m^γ) as γ=0.67^{+0.20}_{-0.17}. This result is clearly consistent at $1\sigma$ with the value γ={6/11}=0.55 predicted by LCDM. A first order expansion of the index γin 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.

7 pages, 4 figures. Added comments on the data of Table I (after eq. (2.16)). Corrected a typo on eq. (2.15). The mathematica files with the numerical analysis of this study may be found at http://nesseris.physics.uoi.gr/growth/growth.htm

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