Deep learning method in testing the cosmic distance duality relation

TL;DR

This paper employs deep learning to test the cosmic distance duality relation by reconstructing luminosity distances from supernovae and comparing them with angular diameter distances from gravitational lensing, revealing model-dependent violations.

Contribution

It introduces a deep learning approach to reconstruct distances from supernovae data and tests DDR violations considering different lens mass models, enhancing analysis precision.

Findings

DDR violation detected in SIS and EPL models at high confidence

DDR verified within 1σ in PL model

Constraints on DDR reach about 10^{-2} precision

Abstract

The cosmic distance duality relation (DDR) is constrained from the combination of type-Ia supernovae (SNe Ia) and strong gravitational lensing (SGL) systems using deep learning method. To make use of the full SGL data, we reconstruct the luminosity distance from SNe Ia up to the highest redshift of SGL using deep learning, then it is compared with the angular diameter distance obtained from SGL. Considering the influence of lens mass profile, we constrain the possible violation of DDR in three lens mass models. Results show that in the SIS model and EPL model, DDR is violated at high confidence level, with the violation parameter $\eta_0=-0.193^{+0.021}_{-0.019}$ and $\eta_0=-0.247^{+0.014}_{-0.013}$, respectively. In the PL model, however, DDR is verified within 1$\sigma$ confidence level, with the violation parameter $\eta_0=-0.014^{+0.053}_{-0.045}$. Our results demonstrate that the constraints on DDR strongly depend on the lens mass models. Given a specific lens mass model, DDR can be constrained at a precision of $\textit{O}(10^{-2})$ using deep learning.