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

In [1] a new method to measure the speed of light through Baryon Acoustic Oscillations (BAO) was introduced. Here, we describe in much more detail the theoretical basis of that method, its implementation, and give some newly updated results about its application to the forecast data. In particular, we will show that SKA will be able to detect a 1% variation (if any) in the speed of light at 3$\sigma$ level. Smaller signals will be hardly detected by already-planned future galaxy surveys, but we give indications about what sensitivity requirements should a survey fulfill in order to be successful.