Spatial variation of fundamental constants: testing models with thermonuclear supernovae

Since Dirac stated his Large Number Hypothesis the space-time variation of fundamental constants has been an active subject of research. Here we analyze the possible spatial variation of two fundamental constants: the fine structure constant {\alpha} and the speed of light c. We study the effects of such variations on the luminosity distance and on the peak luminosity of Type Ia supernovae (SNe Ia). For this, we consider the change of each fundamental constant separately and discuss a dipole model for its variation. Elaborating upon our previous work, we take into account the variation of the peak luminosity of Type Ia supernovae resulting from the variation of each of these fundamental constants. Furthermore, we also include the change of the energy release during the explosion, which was not studied before in the literature. We perform a statistical analysis to compare the predictions of the dipole model for {\alpha} and c variation with the Union2.1 and JLA compilations of SNe Ia. For this, we also allow the nuisance parameters of the distance estimator $\mu_0$ and the cosmological density matter $\Omega_m$ to vary. As a result of our analysis we obtain a first estimate of the possible spatial variation of the speed of light c. On the other hand, we find that there is no significant difference between the several phenomenological models studied here and the standard cosmological model, in which fundamental constants do not vary at all. Thus, we conclude that the actual set of data of Type Ia supernovae does not allow to verify the hypothetical spatial variation of fundamental constants.