Astron. Astrophys. 347, 409-418 (1999)

1. Introduction

The Cosmic Microwave Background (CMB) is a powerful tool for cosmology. As the CMB temperature anisotropies represent the superposition of primary (before matter-radiation decoupling) and secondary (after decoupling) fluctuations, the study of the anisotropies gives a direct insight into both the early Universe (and its initial conditions) and the formation and evolution of cosmic structures. One of the goals of cosmology is to characterise the initial density perturbations which gave rise to those structures: galaxies and galaxy clusters. The statistical properties of the initial perturbations provide part of the necessary information for this characterisation. They can indeed be used to test and constrain the cosmological models and the scenarios of structure formation. The angular power spectrum of the temperature fluctuations is one of the most important statistical quantities for CMB anisotropy studies. In fact, it allows the evaluation of the main cosmological parameters (, , , n,...) defining our Universe (Jungman et al. 1996). Some of the first constraints on the cosmological parameters came from CMB anisotropy measurements made by the COBE satellite (Smoot et al. 1992; Wright et al. 1992). The statistical properties of the CMB anisotropies give us information, in particular, on the physical process at the origin of the initial density fluctuations. Two classes of scenario account for the initial seeds of the structures. One is the "inflationary model" (Guth 1981; Linde 1982) in which the density perturbations result from the quantum fluctuations of scalar fields in the very early Universe. The other invokes the topological defects which themselves correspond to symmetry breaking in the unified theory (cosmic string, textures) (Vilenkin 1985; Bouchet et al. 1988; Stebbins 1988; Turok 1989; Pen et al. 1994). Several studies have shown that the two scenarios predict different angular power spectra (Coulson et al. 1994; Albrecht et al. 1996; Magueijo et al. 1996). These differences of amplitude and/or shape represent rather tight constraints on the models. The statistical nature of the primary density perturbations, and hence their origin, is also encompassed within the distribution of the CMB anisotropies. The brightness, or temperature, distribution is indeed directly induced by the primeval mass or density distribution. If the initial perturbations result from an inflationary process the primary anisotropy distribution is Gaussian. If the perturbations are generated by topological defects the anisotropy distribution is non-Gaussian. The latter predict very specific patterns distinguishable from a Gaussian random field. It is thus necessary to find statistical methods to test for non-gaussianity and to separate primary and secondary non-gaussianity.

Several studies have been performed to test for the CMB gaussianity. Traditional methods use the brightness or temperature distribution and their nth order moments or their cumulants (Ferreira et al. 1997). Other methods are based on the n-point correlation functions or their spherical harmonic transforms (Luo & Schramm 1993; Magueijo 1995; Kogut et al. 1996; Ferreira & Magueijo 1997; Ferreira et al. 1998; Heavens 1998; Spergel & Goldberg 1998). Non-gaussianity can also be tested through topological discriminators based on pattern statistics (Coles 1988; Gott et al. 1990). Alternative methods test the non-gaussianity in the Fourier or wavelet space (Ferreira & Magueijo 1997; Hobson et al. 1998; Forni & Aghanim 1999).

In addition to the intrinsic statistical properties of the CMB anisotropies, the secondary fluctuations associated with cosmic structures (e.g., galaxies and galaxy clusters) induce non-Gaussian signatures which could originate from point-like sources, peaked profiles, or from geometrical characteristics such as sharp edges or specific patterns. Future high sensitivity and high resolution CMB observations (e.g., MAP ¹ and Planck Surveyor ² satellites) will provide data sets which should allow detailed tests of the primary anisotropy distribution. A detailed study of the non-gaussianity associated with secondary sources could be used to discriminate between the inflationary and topological defect models.

The present study deals with this first step: to predict and to specify the non-Gaussian signature of the secondary anisotropies arising from the scattering of CMB photons by the ionised matter in the Universe. We apply the statistical discriminators developed in Forni & Aghanim (1999) to combinations of Gaussian primary and secondary non-Gaussian anisotropies. We take into account the contribution of a population of galaxy clusters through the Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zel'dovich 1980) as well as the effect of a spatially inhomogeneous re-ionisation of the Universe (Aghanim et al. 1996; Gruzinov & Hu 1998; Knox et al. 1998). The non-Gaussian signature due to secondary anisotropies associated with weak gravitational lensing have been investigated in previous studies (Seljak 1996; Bernardeau 1998; Winitzki 1998).

In Sect. 2, we present the astrophysical contributions we take into account in our study. We then briefly present the statistical tests and detection strategy in Sect. 3. We apply our tests to the combinations of primary and secondary anisotropies due to inhomogeneous re-ionisation alone in Sect. 4, and to a configuration including the SZ effect of galaxy clusters in Sect. 5. In Sect. 6, we investigate the detectability of the non-Gaussian signature for a MAP-like and a Planck-like instrumental configuration. Finally, in Sect. 7, we discuss our results and present our conclusions.

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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