Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation

Abstract: Strong gravitational lensing contains key information about cosmic acceleration. Modern and next-generation galaxy imaging surveys are expected to provide high-quality data on $\mathcal{O}(10<sup>5)$ galaxy-galaxy lensing systems. The plethora and complexity of the data are likely to present computational challenges for parameter inference methods for fitting high-dimensional likelihoods, which are often analytically intractable. Neural Ratio Estimation (NRE) efficiently computes individual likelihood ratios that can be combined into population-level posteriors. We use simulations to study the capacity of NRE to jointly predict the dark energy equation-of-state parameter $w$ and the total matter density $Ω<em>{m}$ from lensing images and companion spectroscopic information. We also introduce a post hoc posterior coverage calibration procedure that mitigates the model overconfidence that is typically found in neural density estimation applications. Our experiments show that the errors on both parameters decrease with increasing inference population sizes. In particular, for 100 lenses in a standard $Λ$CDM Universe, our calibrated NRE model achieves median fractional uncertainty of $22.8\%$ in $w$ and $2.9\%$ in $Ω</em>{m}$. This proof of concept demonstrates a potentially scalable approach for efficient cosmological parameter inference with large populations of galaxy-scale lenses observed in future surveys.