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Multiple methods for estimating the bispectrum of the cosmic microwave background with application to the MAXIMA data
Authors:M. G. Santos  A. Heavens  A. Balbi  J. Borrill  P. G. Ferreira  S. Hanany  A. H. Jaffe  A. T. Lee  B. Rabii  P. L. Richards  G. F. Smoot  R. Stompor  C. D. Winant   J. H. P. Wu
Affiliation:Astrophysics &Theoretical Physics, University of Oxford, Oxford OX1 3RH;Department of Physics, One Shields Ave, University of California, Davis, CA 95616, USA;Institute for Astronomy, University of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ;Dipartimento di Fisica, UniversitàTor Vergata, Roma, Via della Ricerca Scientifica, I-00133 Roma, Italy;Center for Particle Astrophysics, 301 Le Conte Hall, University of California, Berkeley, CA 94720-7304, USA;Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA;National Energy Research Scientific Computing Centre, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA;School of Physics and Astronomy, 116 Church St SE, University of Minnesota, Minneapolis, MN 55455, USA;Astrophysics Group, Blackett laboratory, Prince Consort Road, Imperial College, London SW7 2BW;Department of Physics, University of California, Berkeley, CA 94720-7300, USA;Department of Astronomy, 601 Campbell Hall, University of California, Berkeley, CA 94720-3411, USA;Department of Physics, National Taiwan University, No 1 Sec. 4 Roosevelt Road, Taipei 106, Taiwan
Abstract:We describe different methods for estimating the bispectrum of cosmic microwave background data. In particular, we construct a minimum-variance estimator for the flat-sky limit and compare results with previously studied frequentist methods. Application to the MAXIMA data set shows consistency with primordial Gaussianity. Weak quadratic non-Gaussianity is characterized by a tunable parameter   f NL  , corresponding to non-Gaussianity at a level of  ∼10−5 f NL  (the ratio of non-Gaussian to Gaussian terms), and we find limits of   f NL= 1500 ± 950  for the minimum-variance estimator and   f NL= 2700 ± 1650  for the usual frequentist estimator. These are the tightest limits on primordial non-Gaussianity, which include the full effects of the radiation transfer function.
Keywords:methods: data analysis    methods: statistical    cosmic microwave background    early Universe
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