Testing (modified) gravity with 3D and tomographic cosmic shear

TL;DR

This paper compares 3D and tomographic cosmic shear analysis methods for testing gravity, extending the 3D formalism to Horndeski theories, and finds that 3D analysis offers improved constraints by retaining full redshift information.

Contribution

It introduces a 3D formalism for Horndeski gravity in cosmic shear analysis and provides a quantitative comparison with tomographic methods using Fisher forecasts.

Findings

3D analysis constrains Horndeski theories better than tomographic analysis.

The 3D method reduces errors by approximately 20%.

This is the first quantitative comparison of 3D and tomographic cosmic shear forecasts.

Abstract

Cosmic shear is one of the primary probes to test gravity with current and future surveys. There are two main techniques to analyse a cosmic shear survey; a tomographic method, where correlations between the lensing signal in different redshift bins are used to recover redshift information, and a 3D approach, where the full redshift information is carried through the entire analysis. Here we compare the two methods, by forecasting cosmological constraints for future surveys like Euclid. We extend the 3D formalism for the first time to theories beyond the standard model, belonging to the Horndeski class. This includes the majority of universally coupled extensions to $\Lambda$CDM with one scalar degree of freedom in addition to the metric, still in agreement with current observations. Given a fixed background, the evolution of linear perturbations in Horndeski gravity is described by a set of four functions of time only. We model their time evolution assuming proportionality to the dark energy density fraction and place Fisher matrix constraints on the proportionality coefficients. We find that a 3D analysis can constrain Horndeski theories better than a tomographic one, in particular with a decrease in the errors of the order of 20$\%$. This paper shows for the first time a quantitative comparison on an equal footing between Fisher matrix forecasts for both a fully 3D and a tomographic analysis of cosmic shear surveys. The increased sensitivity of the 3D formalism comes from its ability to retain information on the source redshifts along the entire analysis.