Principal Components for Model-Agnostic Modified Gravity with 3x2pt

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 ΛCDM which includes modifications to the growth of structure and lensing of light (ΛCDM+μ₀+Σ₀) using mock Stage-IV data for two simulated cosmologies: the ΛCDM model and Extended Shift Symmetric (ESS) gravity. Under the assumption of a Universe defined by ΛCDM and General Relativity, our method offers constraints on μ₀ 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 fσ₈ measurements, introducing a promising new tool for the analysis of present and future WL and LSS photometric surveys.