Generalization of the Planck radiation law and application to the cosmic microwave background radiation

Within the framework of the recently introduced nonextensive statistical mechanics, we generalize the Planck law for the blackbody radiation. The generalized thermal spectrum contains an additional parameter q, for which q=1 in the Planck limit. For the cosmic microwave background radiation, we find a 95% confidence limit of \ensuremath{\Vert}q-1\ensuremath{\Vert}3.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ from the data of Mather et al. [Astrophys. J. 420, 439 (1994)] that were obtained with the Cosmic Background Explorer satellite, under the assumption that the internal reference of the apparatus has a Planck spectrum.