Measuring the speed of light with cosmological observations: current constraints and forecasts

We measure the speed of light with current observations, such as Type Ia Supernova, galaxy ages, radial BAO mode, as well as simulations of forthcoming redshift surveys and gravitational waves as standard sirens. By means of a Gaussian Process reconstruction, we find that the precision of such measurements can be improved from roughly 6\% and to about $2-2.5\%$ when the gravitational wave simulations are considered, and to $1.5-2\%$ when redshift survey are included in the analysis as well. This result demonstrates that we will be able to perform a cosmological measurement of a fundamental physical constant with significantly improved precision, which will help us underpinning if its value is truly consistent with local measurements, as predicted by the standard model of Cosmology.