Cosmological tests of General Relativity: a principal component analysis

TL;DR

This paper applies principal component analysis to future weak lensing surveys to test deviations from General Relativity, considering systematic effects and parameter degeneracies, and demonstrates its use for efficient data compression.

Contribution

It extends previous PCA analyses by including systematic effects, exploring different parameterizations, and demonstrating PCA as a tool for efficient model constraints in cosmology.

Findings

PCA identifies eigenmodes sensitive to modified gravity signals.

Systematic effects impact the eigenmode structure and parameter constraints.

PCA effectively compresses data for rapid testing of gravity models.

Abstract

The next generation of weak lensing surveys will trace the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. Along with constraining the dynamics of dark energy, they will probe the relations between matter overdensities, local curvature, and the Newtonian potential. We work with two functions of time and scale to account for any modifications of these relations in the linear regime from those in the LCDM model. We perform a Principal Component Analysis (PCA) to find the eigenmodes and eigenvalues of these functions for surveys like DES and LSST. This paper builds on and significantly extends the PCA analysis of Zhao et al. (2009) in several ways. In particular, we consider the impact of some of the systematic effects expected in weak lensing surveys. We also present the PCA in terms of other choices of the two functions needed to parameterize modified growth on linear scales, and discuss their merits. We analyze the degeneracy between the modified growth functions and other cosmological parameters, paying special attention to the effective equation of state w(z). Finally, we demonstrate the utility of the PCA as an efficient data compression stage which enables one to easily derive constraints on parameters of specific models without recalculating Fisher matrices from scratch.