# Cosmic Growth Signatures of Modified Gravitational Strength

## TL;DR

This paper investigates how modifications in gravitational strength over cosmic history affect large-scale structure growth, providing analytical tools and projections for future survey constraints to test gravity theories.

## Contribution

It introduces a parametrization of modified gravity effects via the 'area' of coupling deviations, enabling simplified analysis of their impact on cosmic growth.

## Key findings

- Modifications during matter era can be characterized by a single parameter.
- Future surveys can constrain gravity modifications to within 0.3% accuracy.
- Projected constraints aim for better than 5% uncertainty in gravity tests.

## Abstract

Cosmic growth of large scale structure probes the entire history of cosmic expansion and gravitational coupling. To get a clear picture of the effects of modification of gravity we consider a deviation in the coupling strength (effective Newton's constant) at different redshifts, with different durations and amplitudes. We derive, analytically and numerically, the impact on the growth rate and growth amplitude. Galaxy redshift surveys can measure a product of these through redshift space distortions and we connect the modified gravity to the observable in a way that may provide a useful parametrization of the ability of future surveys to test gravity. In particular, modifications during the matter dominated era can be treated by a single parameter, the "area" of the modification, to an accuracy of $\sim0.3\%$ in the observables. We project constraints on both early and late time gravity for the Dark Energy Spectroscopic Instrument and discuss what is needed for tightening tests of gravity to better than 5% uncertainty.