Deviation from Gaussianity in the cosmic microwave background temperature fluctuations

Armando Bernui; Constantino Tsallis; Thyrso Villela

doi:10.1209/0295-5075/78/19001

All issues

Volume 78 / No 1 (April 2007)

EPL, 78 1 (2007) 19001

Abstract

Issue		EPL Volume 78, Number 1, April 2007


Article Number		19001
Number of page(s)		6
Section		Geophysics, Astronomy and Astrophysics
DOI		https://doi.org/10.1209/0295-5075/78/19001
Published online		19 March 2007

EPL, 78 (2007) 19001

Deviation from Gaussianity in the cosmic microwave background temperature fluctuations

Armando Bernui¹, Constantino Tsallis² and Thyrso Villela¹

¹ Instituto Nacional de Pesquisas Espaciais, Divisão de Astrofísica - Av. dos Astronautas 1758, 12227-010 São José dos Campos, SP, Brazil
² Centro Brasileiro de Pesquisas Físicas - Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil

Received: 6 October 2006
Accepted: 19 February 2007

Abstract

Recent measurements of the temperature fluctuations of the cosmic microwave background (CMB) radiation from the WMAP satellite provide indication of a non-Gaussian behavior. Although the observed feature is small, it is detectable and analyzable. Indeed, the temperature distribution $P^{{\rm CMB}}(\Delta T)$ of these data can be quite well fitted by the anomalous probability distribution emerging within nonextensive statistical mechanics, based on the entropy $S_q \equiv k \{ 1-\int \, \upd x \, [P(x)]^q \} /(q\!-\!1)$ ( $S_1 \!=\! - k \int \, \upd x \, P(x) \, {\rm ln}[P(x)]$ ). For the CMB frequencies analysed, $\nu =$ 40.7, 60.8, and 93.5 GHz, $P^{{\rm CMB}}(\Delta T)$ is well described by $P_{q}(\Delta T) \propto 1/[1+(q-1) B(\nu ) (\Delta T)^{2}]^{1/(q-1)}$ , with $q=1.04 \pm 0.01$ , the strongest non-Gaussian contribution coming from the South-East sector of the celestial sphere. Moreover, Monte Carlo simulations exclude, at the 99% confidence level, $P_{1}(\Delta T) \propto e^{-B(\nu )(\Delta T)^{2}}$ to fit the three-year data.

PACS: 98.80.Es – Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc.) / 98.70.Vc – Background radiations / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems

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