Measuring the speed of light with Baryon Acoustic Oscillations

In this letter we describe a new method to use Baryon Acoustic Oscillations (BAO) to derive a constraint on the possible variation of the speed of light. The method relies on the fact that there is a simple relation between the angular diameter distance $(D_{A})$ maximum and the Hubble function $(H)$ evaluated at the same maximum-condition redshift, which includes speed of light $c$. We note the close analogy of the BAO probe with a laboratory experiment: here we have $D_{A}$ which plays the role of a standard (cosmological) ruler, and $H^{-1}$, with the dimension of time, as a (cosmological) clock. We evaluate if current or future missions such as Euclid can be sensitive enough to detect any variation of $c$.