Concerning parameter estimation using the cosmic microwave background

Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational diculties generally preclude an exact analysis based on pixel values. With the specic goal of testing this kind of approach, we have performed a complete (un-approximated) likelihood analysis combining the COBE, Saskatoon and MAX data sets. We examine in detail the ability of certain approximate techniques based on band{power estimates to recover the full likelihood constraints. The traditional 2 {method does not always nd the same best{t model as the likelihood analysis (a bias), due mainly to the false assumption of Gaussian likelihoods that makes the method overly sensitive to data outliers. Although an improvement, other approaches employing non{Gaussian flat-band likelihoods do not always faithfully reproduce the complete likelihood constraints either; not even when using the exact flat-band likelihood curves. We trace this to the neglect of spectral information by simple flat band{power estimates. A straightforward extension incorporating a local eective slope (of the power spectrum, Cl )p rovides a faithful representation of the likelihood surfaces without signicantly increasing computing cost. Finally, we also demonstrate that the best{t model to this particular data set is a good t, or that the observations are consistent with Gaussian sky fluctuations, according to our statistics.

[1]  James J. Bock,et al.  Constraints on Cosmological Parameters from MAXIMA-1 , 2000 .

[2]  A. Melchiorri,et al.  A flat Universe from high-resolution maps of the cosmic microwave background radiation , 2000, Nature.

[3]  Matias Zaldarriaga,et al.  Current Cosmological Constraints from a 10 Parameter Cosmic Microwave Background Analysis , 2000, astro-ph/0002091.

[4]  N. Suzuki,et al.  Review of Big Bang Nucleosynthesis and Primordial Abundances , 2000, astro-ph/0001318.

[5]  K. Olive,et al.  Primordial nucleosynthesis: Theory and observations , 1999, astro-ph/9905320.

[6]  P. Steinhardt,et al.  Cosmology - The cosmic triangle: Revealing the state of the universe , 1999, astro-ph/9906463.

[7]  J. Bartlett,et al.  An Approximation to the Likelihood Function for Band-Power Estimates of CMB Anisotropies , 1999, astro-ph/9903045.

[8]  A. Jaffe,et al.  Computing challenges of the cosmic microwave background , 1999, Comput. Sci. Eng..

[9]  A. Kogut.  Likelihood Analysis of Mega-Pixel Maps , 1999, astro-ph/9902177.

[10]  O. Lahav,et al.  Joint Estimation of Cosmological Parameters fromCosmic Microwave Background and IRAS Data , 1998 .

[11]  A. Jaffe,et al.  Radical Compression of Cosmic Microwave Background Data , 1998, astro-ph/9808264.

[12]  A. Riess,et al.  Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant , 1998, astro-ph/9805201.

[13]  U. Toronto,et al.  Estimating the power spectrum of the cosmic microwave background , 1997, astro-ph/9708203.

[14]  K. Ganga,et al.  MAX 4 and MAX 5 Cosmic Microwave Background Anisotropy Measurement Constraints on Open and Flat-Λ Cold Dark Matter Cosmogonies , 1997, astro-ph/9708202.

[15]  C. Lineweaver,et al.  What Can Cosmic Microwave Background Observations Already Say about Cosmological Parameters in Open and Critical-Density Cold Dark Matter Models? , 1997, astro-ph/9706077.

[16]  Edward J. Wollack,et al.  A Measurement of the Angular Power Spectrum of the Anisotropy in the Cosmic Microwave Background , 1996, astro-ph/9601197.

[17]  V. Hristov,et al.  Measurements of anisotropy in the cosmic microwave background radiation at degree angular scales near the stars Sigma Herculis and Iota Draconis , 1994, astro-ph/9404072.

[18]  K. Gorski.  On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method , 1994, astro-ph/9403066.

[19]  Martin White,et al.  Window functions for CMB experiments , 1994, astro-ph/9402037.

[20]  H. Lange.  Eine Zwischenbilanz der Umweltbewußtseinsforschung , 2000 .

[21]  A. Banday,et al.  Evolution of large scale structure : from recombination to Garching : proceedings of the MPA-ESO Cosmology Conference : Garching, Germany, 2-7 August 1998 , 1999 .

[22]  to be published , 1995 .

[23]  J. Kurfess,et al.  Accepted for Publication in the Astrophysical Journal Osse Observations of 3c 273 , 1994 .