Growth index after the Planck results

Abstract

The growth index γ_L was proposed to investigate the possible deviation from the standard ΛCDM model and Einstein’s gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of the density contrast through fσ₈(z), where f(z)=dln⁡δ/dln⁡a is the growth rate of matter and σ₈(z) is the rms amplitude of the density contrast δ at the comoving 8h^-1Mpc scale. In this paper, we use the redshift-space distortion data points to study the growth index on the bases of Einstein’s gravity theory and a modified gravity theory under the assumption of f=Ω_m(a)^γ_L. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3 data, cosmic microwave background radiation data from Planck, and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we find the following γ_L values for Einstein’s gravity with a cosmological constant (w=const) dark energy and a modified gravity theory in the 1, 2, and 3σ regions, respectively: 0.675_{-0.0662-0.120-0.155}^{+0.0611+0.129+0.178}, 0.745_{-0.0819-0.146-0.190}^{+0.0755+0.157+0.205}, and 0.555_{-0.0167-0.0373-0.0516}^{+0.0193+0.0335+0.0436}. In Einstein’s gravity theory, the values of the growth index γ_L show an almost 2σ deviation from the theoretical prediction of 6/11 for the ΛCDM model. However, in the modified gravity framework, a deviation from Einstein’s relativity is not detected in the 1σ region. This implies that the currently available cosmic observations do not predict an alternative modified gravity theory beyond the ΛCDM model under Einstein’s gravity, but that the simple assumption of f=Ω_m^γ_L should be improved.