Growth Index after the Planck Results

Abstract

The growth index ${\gamma }_L$ was proposed to investigate the possible deviation from the standard $\Lambda$CDM 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 $f{\sigma }_8(z)$, where $f(z)=d\ln \delta /d\ln a$ is the growth rate of matter and ${\sigma }_8(z)$ is the rms amplitude of the density contrast $\delta$ 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 $f={\Omega }_m(a{)}^{{\gamma }_L}$. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3, cosmic microwave background radiation data from {\it Planck} and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we found the ${\gamma }_L$ values for Einstein's gravity with a cosmological constant, $w=constant$ dark energy and a modified gravity theory in the $1,2,3\sigma$ 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 the Einstein's gravity theory, the values of growth index ${\gamma }_L$ show almost $2\sigma$ deviation from the theoretical prediction 6/11 for the $\Lambda$CDM model. However in the modified gravity framework, a deviation from the Einstein's relativity is not detected in $1\sigma$ region. That implies that the currently available cosmic observations don't expect an alternative modified gravity theory beyond the $\Lambda$CDM model under Einstein's gravity, but that the simple assumption of $f={\Omega }_m^{{\gamma }_L}$ should be improved.

to match the published version, to appear in PRD

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• Coupled dark energy with perturbed Hubble expansion rate
• Testing the effect of $H_0$ on $f{\sigma }_8$ tension using a Gaussian Process method
• Measuring growth index in a universe with massive neutrinos: A revisit of the general relativity test with the latest observations
• Constraining the curvature density parameter in cosmology
• Constraint on $f(R)$ Gravity through the Redshift Space Distortion
• Measuring growth index in a universe with sterile neutrinos
• Precision growth index using the clustering of cosmic structures and growth data
• Cosmic constraint on massive neutrinos in viable f(R) gravity with producing LCDM background expansion
• Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data
• Confronting DGP Braneworld Gravity with Cosmic Observations after Planck Data
• Cluster-Void Degeneracy Breaking: Modified Gravity in the Balance
• Growth index of matter perturbations in the light of Dark Energy Survey
• Observational Constraints on Growth Index with Cosmography
• Exploring the Growth Index ${\gamma }_L$: Insights from Different CMB Dataset Combinations and Approaches
• Data-driven and Almost Model-independent Reconstruction of Modified Gravity
• Interacting parametrized post-Friedmann method