Observational constraint on the varying speed of light theory

TL;DR

This paper tests the varying speed of light theory against multiple cosmological observations and finds that current data strongly support a constant speed of light, challenging the VSL hypothesis.

Contribution

It introduces a VSL dark energy model and uses observational data to constrain the variation of the speed of light, finding it consistent with being constant.

Findings

The variation parameter n is constrained to nearly zero.

The speed of light variation is negligible for redshift z<0.1.

Current data cannot distinguish VSL from standard cosmology.

Abstract

The varying speed of light (VSL) theory is controversial. It succeeds in explaining some cosmological problems, but on the other hand it is excluded by mainstream physics because it will shake the foundation of physics. In the present paper, we devote ourselves to test whether the speed of light is varying from the observational data of the type Ia Supernova, Baryon Acoustic Oscillation, Observational $H(z)$ data and Cosmic Microwave Background (CMB). We select the common form $c(t)=c_0a^n(t)$ with the contribution of dark energy and matter, where $c_0$ is the current value of speed of light, $n$ is a constant, and consequently construct a varying speed of light dark energy model (VSLDE). The combined observational data show a much trivial constraint $n=-0.0033 \pm 0.0045$ at 68.3\% confidence level, which indicates that the speed of light may be a constant with high significance. By reconstructing the time-variable $c(t)$, we find that the speed of light almost has no variation for redshift $z < 10^{-1}$. For high-$z$ observations, they are more sensitive to the VSLDE model, but the variation of speed of light is only in order of $10^{-2}$. We also introduce the geometrical diagnostic $Om (z)$ to show the difference between the VSLDE and $\Lambda$CDM model. The result shows that the current data are difficult to differentiate them. All the results show that the observational data favor the constant speed of light.