Extragalactic Test of General Relativity from Strong Gravitational Lensing by using Artificial Neural Networks

Abstract

This study aims to test the validity of general relativity (GR) on kiloparsec scales by employing a newly compiled galaxy-scale strong gravitational lensing (SGL) sample. We utilize the distance sum rule within the Friedmann-Lema\^{\i}tre-Robertson-Walker metric to obtain cosmology-independent constraints on both the parameterized post-Newtonian parameter $\gamma_{\rm PPN}$ and the spatial curvature $\Omega_{k}$, which overcomes the circularity problem induced by the presumption of a cosmological model grounded in GR. To calibrate the distances in the SGL systems, we introduce a novel nonparametric approach, Artificial Neural Network (ANN), to reconstruct a smooth distance--redshift relation from the Pantheon+ sample of type Ia supernovae. Our results show that $\gamma_{\rm PPN}=1.16_{-0.12}^{+0.15}$ and $\Omega_k=0.89_{-1.00}^{+1.97}$, indicating a spatially flat universe with the conservation of GR (i.e., $\Omega_k=0$ and $\gamma_{\rm PPN}=1$) is basically supported within $1\sigma$ confidence level. Assuming a zero spatial curvature, we find $\gamma_{\rm PPN}=1.09_{-0.10}^{+0.11}$, representing an agreement with the prediction of 1 from GR to a 9.6\% precision. If we instead assume GR holds (i.e., $\gamma_{\rm PPN}=1$), the curvature parameter constraint can be further improved to be $\Omega_k=0.11_{-0.47}^{+0.78}$. These resulting constraints demonstrate the effectiveness of our method in testing GR on galactic scales by combining observations of strong lensing and the distance--redshift relation reconstructed by ANN.