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 $Λ$CDM which includes modifications to the growth of structure and lensing of light ($Λ$CDM$+μ_0+Σ_0$) using mock Stage-IV data for two simulated cosmologies: the $Λ$CDM model and Extended Shift Symmetric (ESS) gravity. Under the assumption of a Universe defined by $Λ$CDM and General Relativity, our method offers constraints on $μ_0$ 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 $fσ_8$ measurements, introducing a promising new tool for the analysis of present and future WL and LSS photometric surveys.

Figures (25)

• Figure 1: Illustration of scale-cuts on a simulated LSST Y1 3$\times$2pt Fourier-space data vector. With full DMO nonlinear modelling but no baryonic mitigation we could retain the navy blue data points (‘baryonic cuts’). With linear DMO modelling only, we could retain the points in red ('linear cuts'). For clarity, we only display the autocorrelations of the cosmic-shear (shape-shape) measurements.
• Figure 2: Simplified example analysis: the simulated data vector (brown, $(\times)$) is shown together with the model data vectors for two data reduction models (orange $(\text{o})$ and blue $(+)$) under the linear (dashed) and nonlinear (dotted) modelling.
• Figure 3: Simplified example analysis: Cholesky-weighted difference vectors $\Delta C^{00}_{\kappa\kappa}(\ell)$ for the simulated data vector (brown, $(\times)$) and for the two data reduction models (orange $(\text{o})$ and blue $(+)$). We also display the Gaussian covariance matrix $\textbf{C}$ used for the Cholesky decomposition.
• Figure 4: Simplified example analysis: The left panel displays a visualisation of the weighted data vector difference $\Delta\mathbf{D}_{\text{ch}}$ (brown) and the weighted model vector differences for the two data reduction models ($\Delta \mathbf{M}^{\text{(1)}}_{\text{ch}}$ in orange, $(\text{o})$, and $\Delta \mathbf{M}^{(2)}_{\text{ch}}$ in blue, $(+)$), in a 3D space in which the axes each represent the value of the data vector difference in one of three $\ell$ bins. These can be compared with the alternate visualisation of the identical quantities in Figure \ref{['fig:Cell_weighted_example']}. The Cartesian basis vectors $[x,y,z]$ are in black, the principal components (PCs) are the green dashed lines, and their orthogonal vector is in green. The equivalent quantities rotated by $\mathbf{U}_{\text{ch}}$ are displayed in the right panel. In a general problem, the space would be $n$ dimensional with $n$ the number of $\ell$ bins.
• Figure 5: Weighted difference between linear and nonlinear model vectors for our three data reduction models ($\Delta\mathbf{M}_{\text{ch}}$, top; see Section \ref{['sec:MG_theory']} for details) and resulting principal components (bottom) for the $0^{\text{th}}$ source and lens redshift bins. The y-axis scale is not shown, as the scales of the shear, cross, and clustering subplots vary significantly.