Model-independent forecasts for the cosmological anisotropic stress

TL;DR

This paper presents a model-independent forecasting method for measuring the cosmological anisotropic stress using future large-scale surveys, relying solely on observable galaxy clustering and lensing data without additional assumptions.

Contribution

It introduces a new approach to forecast constraints on anisotropic stress that does not depend on specific gravity models or initial conditions.

Findings

Future surveys can constrain $ta$ to 30\u0025 if constant.

Constraints improve to less than 10\u0025 for redshift-dependent $ta$.

Constant $ta$ can be measured with 5\u0025 accuracy.

Abstract

The effective anisotropic stress $\eta$ is a key variable in the characterization of many classes of modified gravity theories, as it allows the testing for a long-range force additional to gravity. In this paper we forecast the precision with which future large surveys can determine $\eta$ in a way that only relies on directly observable quantities obtained from the spectroscopic measurements of the clustering of galaxies and the photometric based observation of the projected lensing and galaxy clustering correlations and their cross signal. Our method does not require further assumptions about the initial power spectrum, the modified gravity model, the expansion rate, or the bias. We consider various cases: $\eta$ free to vary in space and time, or with only redshift dependence, or constant. We take as a reference specifications that approximate a Euclid-like photometric or a combined one with a DESI-like spectroscopic survey. Among our results, we find that a future large-scale lensing and clustering survey can constrain $\eta$ to at least 30\% if $z$, $k$ independent, and to less than 10\% on average for the $z$ dependence only, to finally reach 5\% values in the constant case.