Constraining minimally extended varying speed of light by cosmological chronometers

At least one dimensionless physical constant (i.e. a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should be functions of cosmic time to satisfy all known local laws of physics, including special relativity, thermodynamics, and electromagnetism. Adiabaticity is another necessary condition to keep the homogeneity and isotropy of three-dimensional space. To be a self-consistent theory, one should consider cosmic evolutions of physical constants and quantities when one derives Einstein's field equations and their solutions. All these conditions are well-satisfied in the so-called minimally extended varying speed of light (meVSL) model. Unlike other VSL models, we show that the redshift-drift formula of the meVSL model is the same as a standard model. Therefore, we cannot use this as an experimental tool to verify the meVSL. Instead, one can still use the cosmological chronometers (CC) as a model-independent test of the meVSL. The current CC data cannot distinguish meVSL from the standard model (SM) when we adopt the best-fitting values (or Gaussian prior) of H-0 and omega(m0) from the Planck mission. However, the CC data prefer the meVSL when we choose Pantheon22 data.

Automated summary

For the varying speed of light (VSL) models to be phenomenologically feasible, at least one dimensionless physical constant must change. Adiabaticity and the dependence of physical constants and quantities on cosmic time are also important. The minimally extended VSL (meVSL) model satisfies these conditions and the redshift-drift formula is the same as the standard model. However, the meVSL cannot be verified experimentally but can be tested using cosmological chronometers (CC).