Constraint on the minimally extended varying speed of light using time dilations in Type Ia supernovae

ABSTRACT The Friedmann–Lemaître–Robertson–Walker model establishes the correlation between redshifts and distances. It has a metric expansion of space. As a result, the wavelength of photons propagating through the expanding space is stretched, creating the cosmological redshift, z. It also relates the frequency of light detected by a local observer to that emitted from a distant source. In standard cosmology (i.e. a constant speed light model), this relation is given by a factor 1/(1 + z). However, this ratio is modified in the minimally extended varying speed of light model (meVSL, c = c0ab/4) as 1/(1 + z)1 − b/4. This time dilation effect is detected as the observed rate of the time variation in the intensity of emitted radiation. The spectra of Type Ia supernovae (SNe Ia) provide a reliable way to measure the apparent aging rate of distant objects. We use data on 13 high-redshift (0.28 ≤ z ≤ 0.62) SNe Ia to obtain b = 0.198 ± 0.415 at the 1-σ confidence interval. The current data is too sparse to give meaningful constrain on the meVSL and cannot distinguish the meVSL model from the standard model.