The minimally extended Varying Speed of Light (meVSL)

Abstract

Even though there have been various models of the time-varying speed of light (VSL), they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable theory, it should inherit the success of special relativity including Maxwell equations and thermodynamics at least. For this purpose, we adopt the assumption that the speed of light, c̃, i.e., c̃[a], varies for the scale factor, a. The background FLRW universe can be defined by the constant cosmic time hypersurface using physical quantities such as temperature, density, c̃, etc. It is because they evolve in cosmic time and the homogeneity of the Universe demands that they must equal at the equal cosmic time. The variation of c̃ accompanies the joint variations of all related physical constants in order to satisfy the Lorentz invariance, thermodynamics, Bianchi identity, etc. We dub this VSL model as a “minimally extended VSL (meVSL)”. We derive cosmological observables of meVSL and obtain the constraints on the variation of c̃ by using current cosmological observations. Interestingly, both the cosmological redshift z and all geometrical distances except the luminosity distance of meVSL are the same as those of general relativity. However, the Hubble parameter of meVSL is rescaled as H(z) = (1+z)-b/4 H(GR)(z), where H(GR)(z) denotes the Hubble parameter obtained from general relativity. Thus, it might be used as an alternative solution for the tension of the Hubble parameter measurements. In this manuscript, we provide the main effects of the meVSL model on various cosmological observations including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and Δα. Compared to previous VSL models, meVSL might provide alternative solutions for various late time problems of the standard ΛCDM model. This is the main motivation for proposing the meVSL model.

A Viable Varying Speed of Light Model in the RW Metric

“…Thus, the cosmological redshift relation still holds even if we allow the speed of light can vary as a function of cosmic time. These results have been derived before in a so-called meVSL model to satisfy Einstein field equations [20].…”

“…If c is not a constant in cosmic time, then one needs to rederive the Einstein field equations again by including this VSL effect. Previously, we have shown one viable model [20]. Metric and four-position are given by…”

“…2, we review how to derive the cosmological redshift in the RW metric. We extend this idea into the specific time-varying speed of light model (i.e., meVSL [20]) in section 3. In section 4, we explain how we can obtain consistent results in this model.…”

Observational constraints on varying fundamental constants in a minimal CPC model

“…The common feature of these works is to take only one of the couplings as a function of the cosmological time while disregarding possible variations of the others. Variation of more than one of the aforementioned couplings is a possibility that has been studied recently by [80,81,82,83,84,86,85,87,88], which include the cosmological constant Λ-among others-to the set. More specifically, Refs.…”

A viable varying speed of light model in the RW metric

“…We show that the meVSL model provides consistent results for various measurements even if we allow the Table 1 Summary for cosmological evolutions of physical constants and quantities of the meVSL model. These relations satisfy all known local physics laws, including special relativity, thermodynamics, and electromagnetic force [20,38].…”