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.