Analysis of distribution of cosmic microwave background photon in terms of non-extensive statistics and formulas with temperature fluctuation

TL;DR

This paper investigates temperature fluctuations in the cosmic microwave background using non-extensive statistics and convolution integrals, analyzing COBE data to estimate non-extensivity parameters and compare models including the Sunyaev-Zeldovich effect.

Contribution

It introduces a novel approach combining non-extensive statistics with convolution integrals to analyze CMB temperature fluctuations and estimates the non-extensivity parameter from COBE data.

Findings

Estimated |q-1| = 4.4×10^{-5} for temperature fluctuation magnitude

Derived formulas incorporating non-extensive statistics and S-Z effect

Compared new models with standard Planck distribution

Abstract

To take into account the temperature fluctuation in the Planck distribution, we calculate convolution integral with several probability distributions. Using these formula as well the Planck distribution and a formula in the non-extensive statistics, we analyze the data measured by the Cosmic Background Explorer (COBE). Our analysis reveals that the derivation from the Planck distribution is estimated as |q-1| = 4.4\times 10^{-5}, where q means the magnitude of the non-extensivity or the temperature fluctuation, provided that the dimensionless chemical potential proposed by Zeldovich and Sunyaev exists. Comparisons of new formulas and the Planck distribution including the Sunyaev-Zeldovich (S-Z) effect are made.