Temperature Fluctuations of the Cosmic Microwave Background Radiation: A   Case of Nonextensivity?
  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. 
Armando Bernui, Constantino Tsallis, Thyrso Villela