Effective Theory of Dark Energy at Redshift Survey Scales

TL;DR

This paper investigates how future redshift surveys can constrain modifications to gravity at late times, focusing on non-minimal dark matter coupling and using a Fisher matrix analysis to estimate parameter uncertainties.

Contribution

It introduces an effective theory framework for late-time modified gravity with non-minimal dark matter coupling and assesses observational constraints using multiple cosmological probes.

Findings

Unmarginalized 68% CL errors on parameters are around 10^{-2} to 10^{-3}.

Nonminimal dark matter coupling amplifies modified gravity effects, reducing errors.

Parameter degeneracies are significant but can be partially broken by combining probes.

Abstract

We explore the phenomenological consequences of general late-time modifications of gravity in the quasi-static approximation, in the case where cold dark matter is non-minimally coupled to the gravitational sector. Assuming spectroscopic and photometric surveys with configuration parameters similar to those of the Euclid mission, we derive constraints on our effective description from three observables: the galaxy power spectrum in redshift space, tomographic weak-lensing shear power spectrum and the correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy distribution. In particular, with $\Lambda$CDM as fiducial model and a specific choice for the time dependence of our effective functions, we perform a Fisher matrix analysis and find that the unmarginalized $68\%$ CL errors on the parameters describing the modifications of gravity are of order $\sigma\sim10^{-2}$--$10^{-3}$. We also consider two other fiducial models. A nonminimal coupling of CDM enhances the effects of modified gravity and reduces the above statistical errors accordingly. In all cases, we find that the parameters are highly degenerate, which prevents the inversion of the Fisher matrices. Some of these degeneracies can be broken by combining all three observational probes.