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.
