The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models

Details The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models

1993-12-15

arxiv.org/abs/astro-ph/9312033v1

Astrophys.J. 430 (1994) 447-457

Astronomy and Astrophysics

Astrophysics

18 pages; LaTeX; 4 PostScript figures included at the end of the file; SISSA REF.193/93/A and DFPD 93/A/80

Scientific paper

10.1086/174421

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the {\em COBE} DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic inflation we are able to provide a {\it universal} expression for the ensemble averaged three--point function and for the corresponding skewness, which accounts for all primordial second--order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a {\em hierarchical} form. Our results are then specialized to a number of relevant models: power--law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non--Gaussian effects are small: as an example, the {\em mean} skewness is much smaller than the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation field.

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