To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parametrizations 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 parametrized extension to $\mathrm{\Lambda }\mathrm{CDM}$ which includes modifications to the growth of structure and lensing of light ($\mathrm{\Lambda }\mathrm{CDM}+{\mu }_0+{\mathrm{\Sigma }}_0$) using mock stage-IV data for two simulated cosmologies: the $\mathrm{\Lambda }\mathrm{CDM}$ model and extended shift symmetric (ESS) gravity. Under the assumption of a Universe defined by $\mathrm{\Lambda }\mathrm{CDM}$ and general relativity, our method offers constraints on ${\mu }_0$ 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 $f{\sigma }_8$ measurements, introducing a promising new tool for the analysis of present and future WL and LSS photometric surveys.

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• Alternative gravity theories
• Cosmological parameters
• Astrophysical & cosmological simulations