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Since Dirac stated his Large Number Hypothesis the space-time variation offundamental constants has been an active subject of research. Here we analyzethe possible spatial variation of two fundamental constants: the fine structureconstant {\alpha} and the speed of light c. We study the effects of suchvariations on the luminosity distance and on the peak luminosity of Type Iasupernovae (SNe Ia). For this, we consider the change of each fundamentalconstant separately and discuss a dipole model for its variation. Elaboratingupon our previous work, we take into account the variation of the peakluminosity of Type Ia supernovae resulting from the variation of each of thesefundamental constants. Furthermore, we also include the change of the energyrelease during the explosion, which was not studied before in the literature.We perform a statistical analysis to compare the predictions of the dipolemodel for {\alpha} and c variation with the Union2.1 and JLA compilations ofSNe Ia. For this, we also allow the nuisance parameters of the distanceestimator $\mu_0$ and the cosmological density matter $\Omega_m$ to vary. As aresult of our analysis we obtain a first estimate of the possible spatialvariation of the speed of light c. On the other hand, we find that there is nosignificant difference between the several phenomenological models studied hereand the standard cosmological model, in which fundamental constants do not varyat all. Thus, we conclude that the actual set of data of Type Ia supernovaedoes not allow to verify the hypothetical spatial variation of fundamentalconstants.

Spatial variation of fundamental constants: testing models with thermonuclear supernovae