A Simple Test for Non-Gaussianity in Cosmic Microwave Background Radiation Measurements

Abstract

We propose a set of statistics S q for detecting non-gaussianity in CMBR anisotropy data sets. These statistics are both simple and, according to calculations over a space of linear combinations of three-point functions, nearly optimal at detecting certain types of non-gaussian features. We apply S 3 to the UCSB SP91 experiment and find that the mean of the four frequency channels is by this criterion strongly non-gaussian. Such an observation would be highly unlikely in a gaussian theory with a small coherence angle, such as standard (n = 1, Ω b = .05, h = .5, Λ = 0) inflation. We cannot conclude that the non-gaussianity is cosmological in origin, but if we assume it due instead to foreground contamination or instrumental effects, and remove the points which are clearly responsible for the non-gaussian behavior, the rms of the remaining fluctuations is too small for consistency with standard inflation at high confidence. Further data are clearly needed however, before definitive conclusions may be drawn. We also generalize the ideas behind this statistic to non-gaussian features that might be detected in other experimental schemes.

Testing for the Gaussian nature of cosmological density perturbations through the three-point temperature correlation function

“…The results obtained from Eqs. (9) and (13) strongly suggest that the general form of the three-point function, expressed in terms of two-point functions, is given by (18) analysis of the South Pole data set shows that the quality of fit to non-Gaussian distributions is superior to the quality of Gaussian assumptions for this data set [22]. Although at the present stage the experiments are inconclusive due to possible foreground contaminations, nevertheless they give us hope that the question of Gaussian behavior might be resolved experimentally in the near future.…”

A model for the infrared emission of FSC 10214+4724

“…At the time of its discovery it was thought to be one of the most luminous objects in the Universe. It was later found to be gravitationally lensed by a factor of between 10-100 (Broadhurst & Lehar 1995;Graham & Liu 1995;Serjeant et al 1995;Eisenhardt et al 1996). It is still the best-studied ultraluminous infrared galaxy at that redshift.…”

A spectroscopic study of IRAS F10214 + 4724

“…Elston et al 1994;Trentham 1995), the first direct empirical evidence of strong gravitational lensing was provided by a deep near-infrared image (Matthews et al 1994), which revealed an arc-like structure centred on a galaxy close to the line of sight to F10214 þ 4724. Several sets of authors published lensing interpretations (Broadhurst & Lehár 1995;Graham & Liu 1995;Serjeant et al 1995), which were confirmed by the appearance of the HST image obtained by Eisenhardt et al (1996): this image contained highly elliptical, high-surfacebrightness features characteristic of strong lensing, as well as a clear counterimage. These papers also attempted to constrain the redshift of the system responsible for the gravitational lensing, our contribution (Serjeant et al 1995) being spectroscopy of two galaxies projected Ϸ1 and Ϸ3 arcsec from F10214 þ 4724.…”

“…We assume a Hubble constant of H 0 ¼ 50 h 50 km s ¹1 Mpc ¹1 with Q 0 ¼ 1, Q L ¼ 0. If we assume that the starburst region undergoes a net gravitational magnification of M Շ 10 (Downes et al 1995;Graham & Liu 1995;Green & Rowan-Robinson 1996), and that aperture corrections are negligible, we obtain a star formation rate of տ 20h ¹2 50 M ᭪ per year. This corresponds to a starburst luminosity of տ 2:6 × 10 11 h ¹2 50 L ᭪ (e.g.…”