Testing the speed of light over cosmological distances: the combination of strongly lensed and unlensed supernova Ia

TL;DR

This paper proposes a novel method to measure the speed of light over cosmological distances using strongly lensed supernovae Ia, potentially testing variations in fundamental constants with future surveys like LSST.

Contribution

It introduces an original approach combining gravitational lensing and supernova observations to estimate the speed of light at different redshifts, which has not been explored before.

Findings

Predicted constraints on Δc/c at the level of 10^{-3} with LSST data.

Demonstrated the feasibility of using lensed SNe Ia to test for variations in fundamental constants.

Discussed the potential of future surveys to detect hypothetical changes in the speed of light.

Abstract

Probing the speed of light is as an important test of General Relativity but the measurements of $c$ using objects in the distant universe have been almost completely unexplored. In this letter, we propose an idea to use the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernova acting as background sources to estimate the speed of light. This provides an original method to measure the speed of light using objects located at different redshifts which emitted their light in a distant past. Moreover, we predict that strongly lensed SNe Ia observed by the LSST would produce robust constraints on $\Delta c/c$ at the level of $10^{-3}$. We also discuss whether the future surveys such as LSST may succeed in detecting any hypothetical variation of $c$ predicted by theories in which fundamental constants have dynamical nature.