Probing the constancy of the speed of light with future galaxy survey : the case of SKA and Euclid

In [V. Salzano, M. P. Dąbrowski, and R. Lazkoz, Phys. Rev. Lett. 114, 101304 (2015)] a new method to measure the speed of light through baryon acoustic oscillations was introduced. Here, we describe in much more detail the theoretical basis of that method and its implementation, and we give some newly updated results about its application to forecast data. In particular, we show that SKA will be able to detect a 1% variation (if any) in the speed of light at the 3σ level. Smaller signals will be hardly detectable by already-planned future galaxy surveys, but we give indications of what sensitivity requirements a survey should fulfill in order to be successful.