Characteristic Angular Scales in Cosmic Microwave Background Radiation

Abstract

We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from {\it Wilkinson Microwave Anisotropy Probe}. We show that the angular fluctuations of the temperature is a Markov process with a {\it Markov angular scale}, ${\Theta }_{\mathrm{Markov}}=1.01_{-0.07}^{+0.09}$. We characterize the complexity of the CMB fluctuations by means of a Fokker-Planck or Langevin equation and measure the associated Kramers-Moyal coefficients for the fluctuating temperature field $T(\hat{n})$ and its increment, $\Delta T=T({\hat{n}}_1)-T({\hat{n}}_2)$. Through this method we show that temperature fluctuations in the CMB has fat tails compared to a Gaussian distribution.

10 pages, 8 figures Accepted in J. Stat. Mech

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