  Temperature maps of the Cosmic Microwave Background (CMB) radiation, as those
obtained by the Wilkinson Microwave Anisotropy Probe (WMAP), provide one of the
most precise data sets to test fundamental hypotheses of modern cosmology. One
of these issues is related to the statistical properties of the CMB temperature
fluctuations, which would have been produced by Gaussian random density
fluctuations when matter and radiation were in thermal equilibrium in the early
Universe. We analysed here the WMAP data and found that the distribution of the
CMB temperature fluctuations P^{CMB}(Delta T) can be quite well fitted by the
anomalous temperature distribution emerging within nonextensive statistical
mechanics. This theory is based on the nonextensive entropy S_q = k (1 - \int
dx [P_q(x)]^q) /(q-1), with the Boltzmann-Gibbs expression as the limit case q
-> 1. For the frequencies investigated (\nu= 40.7, 60.8, and 93.5 GHz), we
found that P^{CMB}(Delta T) is well described by P_q(Delta T) \propto 1/[1 +
(q-1) B(\nu) (Delta T)^2]^{1/(q-1)}, with q = 1.055 \pm 0.002, which exclude,
at the 99% confidence level, exact Gaussian temperature distributions
P^{Gauss}(Delta T) \propto e^{- B(\nu) Delta T^2}, corresponding to the q -> 1
limit, to properly represent the CMB temperature fluctuations measured by WMAP.
