# Probing the cosmic distance duality relation using time delay lenses

## TL;DR

This paper tests the cosmic distance duality relation using strong gravitational lensing and supernova data, finding no significant deviation from the standard model within 2 sigma confidence, thus supporting its validity.

## Contribution

It introduces a new method combining lensing and supernova observations with Gaussian Process to test the CDDR in a model-independent way.

## Key findings

- No deviation of CDDR detected within 2σ confidence
- Combined datasets are consistent with the standard value η=1
- Method validated with simulated datasets

## Abstract

The construction of the cosmic distance-duality relation (CDDR) has been widely studied. However, its consistency with various new observables remains a topic of interest. We present a new way to constrain the CDDR $\eta(z)$ using different dynamic and geometric properties of strong gravitational lenses (SGL) along with SNe Ia observations. We use a sample of $102$ SGL with the measurement of corresponding velocity dispersion $\sigma_0$ and Einstein radius $\theta_E$. In addition, we also use a dataset of $12$ two image lensing systems containing the measure of time delay $\Delta t$ between source images. Jointly these two datasets give us the angular diameter distance $D_{A_{ol}}$ of the lens. Further, for luminosity distance, we use the $740$ observations from JLA compilation of SNe Ia. To study the combined behavior of these datasets we use a model independent method, Gaussian Process (GP). We also check the efficiency of GP by applying it on simulated datasets, which are generated in a phenomenological way by using realistic cosmological error bars. Finally, we conclude that the combined bounds from the SGL and SNe Ia observation do not favor any deviation of CDDR and are in concordance with the standard value ($\eta=1$) within $2\sigma$ confidence region, which further strengthens the theoretical acceptance of CDDR.