A. Gangui et al., THE 3-POINT CORRELATION-FUNCTION OF THE COSMIC MICROWAVE BACKGROUND IN INFLATIONARY MODELS, The Astrophysical journal, 430(2), 1994, pp. 447-457
We analyze the temperature three-point correlation function and the sk
ewness of the cosmic microwave background, providing general relations
in terms of multipole coefficients. We then focus on applications to
large angular scale anisotropies, such as those measured by the COBE D
MR, 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 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 hierarchical form. Our results are then specialized t
o a number of relevant models: power-law inflation driven by an expone
ntial potential, chaotic inflation with a quartic and quadratic potent
ial, and a particular case of hybrid inflation. In all these cases non
-Gaussian effects are small: as an example, the mean skewness is much
smaller than the cosmic rms skewness implied by a Gaussian temperature
fluctuation field.