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 ^ { \text { 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 } \equiv k\ { 1 - \int dx [ P _ { q } ( x ) ] ^ { q } \ } / ( q - 1 ) , with the Boltzmann-Gibbs expression as the limit case q \to 1 .
For the frequencies investigated ( \nu = 40.7 , 60.8 , and 93.5 GHz ) , we found that P ^ { \text { 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 ^ { \text { Gauss } } ( \Delta T ) \propto e ^ { - B ( \nu ) \Delta T\ > ^ { 2 } } , corresponding to the q \to 1 limit , to properly represent the CMB temperature fluctuations measured by WMAP .