Is the CMB shift parameter connected with the growth of cosmological perturbations?

TL;DR

This paper demonstrates that in general relativity, models with identical matter density and CMB shift parameter exhibit similar growth of cosmological perturbations despite differences in dark energy evolution, linking geometric and dynamical tests.

Contribution

It numerically verifies the connection between the CMB shift parameter and perturbation growth, offering a new cosmological test of general relativity.

Findings

Models with same $ m \Omega_m$ and $R$ have similar perturbation growth within 8%.

Dark energy evolution differences do not significantly affect perturbation growth.

Provides a method to test GR using geometric and dynamical cosmological data.

Abstract

We verify numerically that in the context of general relativity (GR), flat models which have the same $\Omega_{\rm m}$ and CMB shift parameter $R$ but different $H(a)$ and $w(a)$ also have very similar (within less than 8%) growth of perturbations even though the dark energy density evolution is quite different. This provides a direct connection between geometrical and dynamical tests of dark energy and may be used as a cosmological test of general relativity.