Constraining a possible time-variation of the speed of light along with the fine-structure constant using strong gravitational lensing and Type Ia supernovae observations

TL;DR

This study investigates potential time variations of the speed of light and fine-structure constant using strong gravitational lensing and supernova data, finding no significant evidence for variation.

Contribution

It introduces a new method combining gravitational lensing and supernova observations to constrain variations in fundamental constants over time.

Findings

No strong evidence for variation of the speed of light.

The method effectively constrains fundamental constant variations.

Sub-sample analysis improves understanding of system differences.

Abstract

The possible time variation of the fundamental constants of nature has been an active subject of research since the large-number hypothesis was proposed by Dirac. In this paper, we propose a new method to investigate a possible time variation of the speed of light ($c$) along with the fine-structure constant ($\alpha$) using Strong Gravitational Lensing (SGL) and Type Ia Supernovae (SNe Ia) observations. We assume a general approach to describe the mass distribution of lens-type galaxies, the one in favor of the power-law index model (PLAW). We also consider the runaway dilaton model to describe a possible time-variation of $\alpha$. In order to explore the results deeply, we split the SGL sample into five sub-samples according to the lens stellar velocity dispersion and three sub-samples according to lens redshift. The results suggest that it is reasonable to treat the systems separately, but no strong indication of varying $c$ was found.