Linear and non-linear Modified Gravity forecasts with future surveys

TL;DR

This paper forecasts the ability of future surveys like Euclid, SKA, and DESI to constrain modified gravity parameters using galaxy clustering and weak lensing data, emphasizing the importance of non-linear scales and parameter decorrelation.

Contribution

It introduces a method to forecast constraints on modified gravity functions using binned redshift data, incorporating non-linear effects and parameter decorrelation techniques.

Findings

Future surveys can constrain current $\eta$ and $\mu$ to 2-5\% with linear scales.

Including non-linear scales improves sensitivity to about 1\\%.

Non-linear treatment reduces parameter degeneracies significantly.

Abstract

Modified Gravity theories generally affect the Poisson equation and the gravitational slip (effective anisotropic stress) in an observable way, that can be parameterized by two generic functions ($\eta$ and $\mu$) of time and space. We bin the time dependence of these functions in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, treated with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. Our results show that $\eta$ and $\mu$ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further decorrelate parameters with a Zero-phase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We also extend the analysis to two particular parameterizations of the time evolution of $\mu$ and $\eta$ and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of $\eta$ and $\mu$ at the $2-5\%$ level when using only linear scales (wavevector k < 0.15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about $1\%$ when non-linearities are included.