Temperature fluctuations of the cosmic microwave background radiation: A case of non-extensivity?

Abstract

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. We analysed here the WMAP data and found that the distribution of the CMB temperature fluctuations P CMB ( Δ T ) can be quite well fitted by the anomalous temperature distribution emerging within non-extensive statistical mechanics. This theory is based on the non-extensive entropy S q ≡ k { 1 − ∫ d x [ P q ( x ) ] q } / ( q − 1 ) , with the Boltzmann–Gibbs expression as the limit case q → 1 . For the frequencies investigated ( ν = 40.7 , 60.8, and 93.5 GHz), we found that P CMB ( Δ T ) is well described by P q ( Δ T ) ∝ 1 / [ 1 + ( q − 1 ) B ( ν ) Δ T 2 ] 1 / ( q − 1 ) , with q = 1.045 ± 0.005 , which indicate, at the 99% confidence level, that Gaussian temperature distributions P Gauss ( Δ T ) ∝ e − B ( ν ) Δ T 2 , corresponding to the q → 1 limit, do not properly represent the CMB temperature fluctuations measured by WMAP.