On the consistency of the expansion with the perturbations

TL;DR

This paper constrains the growth index parameters gamma_0 and gamma_1 using background expansion data, analyzing their implications for models within and outside General Relativity, and discusses the challenges for modified gravity models.

Contribution

It systematically constrains the growth index parameters and explores their implications for different gravity models using background expansion data.

Findings

Favored models within GR have gamma_1 ≈ -0.02.

Lower bounds gamma_0 > 0.53 and gamma_1 > -0.15 are established.

Modified gravity models crossing G_{eff}=G at low redshifts are problematic.

Abstract

Assuming a simple form for the growth index gamma(z) depending on two parameters gamma_0 = gamma(z=0) and gamma_1 = gamma'(z=0), we show that these parameters can be constrained using background expansion data. We explore systematically the preferred region in this parameter space. Inside General Relativity we obtain that models with a quasi-static growth index and gamma_1 = -0.02 are favoured. We find further the lower bounds gamma_0 > 0.53 and gamma_1 > -0.15 for models inside GR. Models outside GR having the same background expansion as LCDM and arbitrary gamma(z) with gamma_0 = gamma_0^{LCDM}, satisfy G_{eff,0}>G for gamma_1 > gamma_1^{LCDM}, and G_{eff,0}<G for gamma_1 < gamma_1^{LCDM}. The first models will cross downwards the value G_{eff}=G on very low redshifts z<0.3, while the second models will cross upwards G_{eff}=G in the same redshift range. This makes the realization of such modified gravity models even more problematic.