Temperature Fluctuations of the Cosmic Microwave Background Radiation: A Case of Nonextensivity?

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, 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^{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 = k (1 - \int dx [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}(Delta T) is well described by P_q(Delta T) \propto 1/[1 + (q-1) B(ν) (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^{Gauss}(Delta T) \propto e^{- B(ν) Delta T^2}, corresponding to the q -> 1 limit, to properly represent the CMB temperature fluctuations measured by WMAP.

arXiv comment5 pages, 2 Postscript figures

References in corpus (33)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Emission
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Tests of Gaussianity
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Dynamical foundations of nonextensive statistical mechanics
• Detection of non-Gaussianity in the WMAP 1-year data using spherical wavelets
• Nonextensivity and multifractality in low-dimensional dissipative systems
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• Measuring primordial non-Gaussianity in the cosmic microwave background
• Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
• Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
• Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton
• Asymmetries in the local curvature of the WMAP data
• Non-Gaussianity of the derived maps from the first-year WMAP data
• Evidence for non-Gaussianity in the COBE DMR Four Year Sky Maps
• The Hot and Cold Spots in the WMAP Data are Not Hot and Cold Enough
• Higher Criticism Statistic: Detecting and Identifying Non-Gaussianity in the WMAP First Year Data
• Fluxes of cosmic rays: A delicately balanced stationary state
• Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos
• Phase Correlations in Cosmic Microwave Background Temperature Maps
• The Edge of Quantum Chaos
• Multiplicative noise: A mechanism leading to nonextensive statistical mechanics
• Numerical indications of a q-generalised central limit theorem
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: On-Orbit Radiometer Characterization
• The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps
• CMB Polarization Experiments
• Search for Cosmic Strings in CMB Anisotropies
• Primordial magnetic field and non-Gaussianity of the 1-year Wilkinson Microwave Anisotropy Probe (WMAP) data
• On the CMB large-scales angular correlations
• The Multipole Vectors of WMAP, and their frames and invariants
• Foreground contributions to the Cosmic Microwave Background

Cited by in corpus (18)

• Cosmological parameter analyses using transversal BAO data
• Mapping the large-scale anisotropy in the WMAP data
• Alignment tests for low CMB multipoles
• A note on q-Gaussians and non-Gaussians in statistical mechanics
• Can a primordial magnetic field originate large-scale anomalies in WMAP data?
• Tomographic analyses of the CMB lensing and galaxy clustering to probe the linear structure growth
• Nonextensive distributions of rotation periods and diameters of asteroids
• Deviation from Gaussianity in the cosmic microwave background temperature fluctuations
• Time Evolution of Temperature Fluctuation in a Non-Equilibrated System
• Searching for non-Gaussianity in the WMAP data
• Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator
• Tomographic local 2D analyses of the WISExSuperCOSMOS all-sky galaxy catalogue
• Nonextensive Statistical Analysis of Meteor Showers and Lunar Flashes
• Primordial Non-Gaussianities of inflationary step-like models
• Non-Gaussian Effects of the Saha's Ionization in the Early Universe
• A Study of Gaussianity in CMB band maps
• Crab pulsar spectrum: a non-extensive approach
• 25 years of Cosmic Microwave Background research at INPE