The significance of measuring cosmological time dilation in the Dark Energy Survey Supernova Program

TL;DR

This paper examines the observational evidence for cosmological time dilation and potential variations in fundamental constants like the speed of light and gravitational constant using Dark Energy Survey supernova data.

Contribution

It provides the first analysis of supernova data supporting possible variations in fundamental constants over cosmic time within a varying speed of light framework.

Findings

Speed of light may be 0.4% to 2.2% slower at redshift 2.

Newton's gravitational constant may have decreased by 1.7% to 8.4%.

Results are consistent with previous studies but not conclusive.

Abstract

In the context of the dispersion relation $c = \lambda \nu$ and considering an expanding universe where the observed wavelength today is redshifted from the emitted wavelength by $\lambda_{0} = \lambda_{\text{emit}} (1+z)$, to keep $c$ constant, it must be that $\nu_{0} = \nu_{\text{emit}} /(1+z)$. However, although the theory for wavelength in the RW metric includes the cosmological redshift, the same is not simply deduced for frequency (the inverse of time). Instead, cosmological time dilation $T_{0} = T_{\text{emit}} (1+z)$ is an additional assumption made to uphold the hypothesis of constant speed of light rather than a relation directly derived from the RW metric. Therefore, verifying cosmological time dilation observationally is crucial. The most recent data on supernovae for this purpose was released recently by the Dark Energy Survey. Results from the i-band specifically support variations in the speed of light within 1-$\sigma$. We used these observations to investigate variations in various physical quantities, including $c$ and $G$, using the minimally extended varying speed of light model. The speed of light was $0.4$\% to $2.2$\% slower, and Newton's constant may have decreased by $1.7$\% to $8.4$\% compared to their current values at redshift $2$. These findings, consistent with previous studies, hint at resolving tensions between different $\Lambda$CDM cosmological backgrounds but are not yet conclusive evidence of a varying speed of light, as the full-band data aligns with standard model cosmology. However, the data remains valuable for testing variations in fundamental constants over cosmic time. Future analyses, particularly with more refined redshift data, may provide clearer insights into these potential changes.