New measures to test modified gravity cosmologies

TL;DR

This paper introduces new phase diagrams to test modified gravity models against cosmological observations, considering deviations in both background and perturbation evolutions, aiding future large-scale structure data analysis.

Contribution

It develops generalized phase diagrams incorporating background and perturbation deviations in modified gravity, extending beyond standard assumptions.

Findings

Deviations from $ m extLambda$CDM are mapped in $ m extalpha$-$f m extsigma_8$ and $ m H$-$f m extsigma_8$ diagrams.

Specific Horndeski models show characteristic signatures in these diagrams.

Predicted deviations can help future observations constrain or exclude modified gravity theories.

Abstract

The observed accelerated expansion of the Universe may be explained by dark energy or the breakdown of general relativity (GR) on cosmological scales. When the latter case, a modified gravity scenario, is considered, it is often assumed that the background evolution is the same as the $\Lambda$CDM model but the density perturbation evolves differently. In this paper, we investigate more general classes of modified gravity, where both the background and perturbation evolutions are deviated from those in the $\Lambda$CDM model. We introduce two phase diagrams, $\alpha{\rm-}f\sigma _8$ and $H{\rm-}f\sigma _8$ diagrams; $H$ is the expansion rate, $f\sigma_8$ is a combination of the growth rate of the Universe and the normalization of the density fluctuation which is directly constrained by redshift-space distortions, and $\alpha$ is a parameter which characterizes the deviation of gravity from GR and can be probed by gravitational lensing. We consider several specific examples of Horndeski's theory, which is a general scalar-tensor theory, and demonstrate how deviations from the $\Lambda$CDM model appears in the $\alpha{\rm-}f\sigma _8$ and $H{\rm-}f\sigma _8$ diagrams. The predicted deviations will be useful for future large-scale structure observations to exclude some of the modified gravity models.