Principal Components for Model-Agnostic Modified Gravity with 3x2pt

Abstract

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method for data reduction. This Principal Component Analysis (PCA)-based framework extracts key features in the matter power spectrum arising from nonlinear effects in a set of representative gravity theories. By performing the analysis in the space of principal components, we can replace sweeping `linear-only' scale cuts with targeted cuts on the transformed data vector, ultimately reducing parameter bias and significantly tightening constraints. We forecast constraints on a minimal parameterised extension to $\hat{I}›$CDM which includes modifications to the growth of structure and lensing of light ($\hat{I}›$CDM$+\hat{I}{¼}_0+\hat{I}{\pounds }_0$) using mock Stage-IV data for two simulated cosmologies: the $\hat{I}›$CDM model and Extended Shift Symmetric (ESS) gravity. Under the assumption of a Universe defined by $\hat{I}›$CDM and General Relativity, our method offers constraints on $\hat{I}{¼}_0$ a factor of 1.65 tighter than traditional linear-only scale cuts. Crucially, our approach also provides the necessary constraining power to break key degeneracies in modified gravity without relying on $f\ddot{I}{ƒ}_8$ measurements, introducing a promising new tool for the analysis of present and future WL and LSS photometric surveys.

22 pages, 14 figures (excluding appendices). Resubmitted to correct typo in section IVE