# Optimising growth of structure constraints on modified gravity

## TL;DR

This paper uses growth of structure data and Solar System bounds to constrain Horndeski theories of dark energy, showing that modifications to gravity are tightly restricted but still allow some deviations from standard cosmology.

## Contribution

It introduces a combined analysis of growth data and Solar System bounds to improve constraints on modified gravity theories, especially Horndeski models.

## Key findings

- Solar System bounds do not exclude suppressed growth at low redshifts.
- The gravitational slip parameter is constrained to be very close to unity.
- Growth data suggests a possible fifth force contribution at low redshifts.

## Abstract

We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate $f$ and the amplitude of matter fluctuations $\sigma_8$ from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on the variation of the Newton constant. This analysis allows us to conclude that: $i)$ despite firmly restricting the predictions of weaker gravity, the inclusion of the Solar System bound does not prevent suppressed growth relative to the standard model $\Lambda$CDM at low redshifts; $ii)$ the same bound in conjunction with the growth of structure data strongly restricts the redshift evolution of the gravitational slip parameter to be close to unity and the present value is constrained to one at the $10^{-3}$ level; $iii)$ the growth of structure data favours a fifth force contribution to the effective gravitational coupling at low redshifts and at more than one sigma at present time.