Growth index after the Planck results

Abstract

The growth index γL 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 density contrast through f σ8(z), where f (z) = d ln δ/d ln a is the growth rate of matter and σ8(z) is the rms amplitude of the density contrast δ at the comoving 8h −1 Mpc 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 = Ωm(a) γ L . The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3, cosmic microwave background radiation data from Planck and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we found the γL values for Einstein's gravity with a cosmological constant, w = constant dark energy and a modified gravity theory in the 1, 2, 3σ regions respectively: 0.675 −0.0167−0.0373−0.0516 . In the Einstein's gravity theory, the values of growth index γL show almost 2σ deviation from the theoretical prediction 6/11 for the ΛCDM model. However in the modified gravity framework, a deviation from the Einstein's relativity is not detected in 1σ region. That implies that the currently available cosmic observations don't expect an alternative modified gravity theory beyond the ΛCDM model under Einstein's gravity, but that the simple assumption of f = Ω γ L m should be improved.

Growth index of matter perturbations in the light of Dark Energy Survey

“…Obviously, we found a small but non-zero deviation from GR (γ GR ≈ 6/11), where the confidence level lies in the interval ∼ 1.3σ − 2σ. Such a small discrepancy between the predicted and observationally fitted value of γ has also been reported in several studies [58], [59] and [60]. Moreover, the intrinsic differences of the bias models are absorbed in the fitted value of the dark-matter halo mass in which LRGs survive, and which belongs in the range ∼ 6.2 × 10 12 h −1 M ⊙ − 1.2 × 10 13 h −1 M ⊙ .…”

Measuring growth index in a Universe with sterile neutrinos

“…[13], in which the constraint result of γ from the RSD measurements (10 f σ 8 data in total) combined with the SN, baryon acoustic oscillation (BAO), and Planck data is also discrepant from the GR expected value at about the 2-3σ level.…”

Constraints onf(R)gravity through the redshift space distortion

“…Therefore, the combination σ g 8 β ¼ fσ 8 is independent of galaxy bias in the linear case [3]. The redshift space distortion data are useful to constrain the cosmological parameters space [4]. In this paper, we use the ten fσ 8 ðzÞ data points as given in Table I for constraining the model parameter space. Because of the degeneracies between dark energy and a modified gravity model at the background level, we mainly focus on a specific family of fðRÞ models, which produce the ΛCDM background expansion history [11][12][13].…”