SKEWNESS IN THE COSMIC MICROWAVE BACKGROUND ANISOTROPY FROM AN INFLATIONARY GRAVITY-WAVE BACKGROUND

In the context of inflationary scenarios, the observed large angle ani sotropy of the cosmic microwave background (CMB) temperature is believ ed to probe the primordial metric perturbations from inflation. Althou gh the perturbations from inflation are expected to be Gaussian random fields, there remains the possibility that nonlinear processes at lat er epochs induce ''secondary'' non-Gaussian features in the correspond ing CMB anisotropy maps. The non-Gaussianity induced by the nonlinear gravitational instability of scalar (density) perturbations has been i nvestigated in the existing literature. In this paper, we highlight an other source of non-Gaussianity arising out of higher-order scattering of CMB photons off the metric perturbations. We provide a simple and elegant formalism for deriving the CMB temperature fluctuations arisin g due to the Sachs-Wolfe effect beyond the linear order. In particular , we derive the expression for the second-order CMB temperature fluctu ations. The multiple scattering effect pointed out in this paper leads to the possibility that tensor metric perturbations, i.e. gravity wav es, which do not exhibit gravitational instability can still contribut e to the skewness in the CMB anisotropy maps. We find that in a flat O mega = 1 universe the skewness in the CMB contributed by gravity waves via the multiple scattering effect is comparable to that from the gra vitational instability of scalar perturbations for equal contributions of the gravity waves and scalar perturbations to the total rms CMB an isotropy. The secondary skewness is found to be smaller than the cosmi c variance leading to the conclusion that inflationary scenarios do pr edict that the observed CMB anisotropy should be statistically consist ent with a Gaussian random distribution. [S0556-2821(97)04320-8].