3D Weak Lensing: Modified Theories of Gravity

TL;DR

This paper explores how 3D weak lensing surveys can constrain modified gravity theories, specifically $f(R)$ and dilaton models, by modeling matter power spectra and using Fisher analysis to forecast parameter bounds.

Contribution

It introduces a 3D weak lensing analysis framework with spherical Fourier-Bessel expansion to constrain MG theories, including detailed modeling and forecasted constraints.

Findings

Constraints on $f_{R_0}$ can reach below $5 imes 10^{-6}$ at 3$\sigma$ confidence.

Higher angular harmonics improve constraints, making them comparable to solar-system tests.

The method is extendable to other MG theories like K-mouflage.

Abstract

Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large scale structure (LSS) as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity (GR). Employing a three-dimensional (3D) analysis based on the spherical Fourier-Bessel (sFB) expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution $\sigma_{\epsilon}$ of source galaxies. Here we focus on two classes of screened theories of gravity: i) $f(R)$ chameleon models and ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of matter power-spectrum with redshift in these theories. Using a Fisher information matrix based approach, we show that for an all-sky spectroscopic survey, the parameter $f_{R_0}$ can be constrained in the range $f_{R_0}< 5\times 10^{-6}(9\times 10^{-6})$ for $n=1(2)$ with a 3$\sigma$ confidence level. This can be achieved by using relatively low order angular harmonics $\ell<100$. Including higher order harmonics $\ell>100$ can further tighten the constraints, making them comparable to current solar-system constraints. We also employ a Principal Component Analysis (PCA) in order to study the parameter degeneracies in the MG parameters. Our results can trivially be extended to other MG theories, such as the K-mouflage models. The confusion from intrinsic ellipticity correlation and modification of the matter power-spectrum at small scale due to feedback mechanisms is briefly discussed.