Skewness in the cosmic microwave background anisotropy from an inflationary gravity wave background

In the context of inflationary scenarios, the observed large angle anisotropy of the cosmic microwave background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from inflation are expected to be Gaussian random fields, there remains the possibility that nonlinear processes at later epochs induce “secondary” non-Gaussian features in the corresponding CMB anisotropy maps. The non-Gaussianity induced by the nonlinear gravitational instability of scalar (density) perturbations has been investigated in the existing literature. In this paper, we highlight another 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 arising due to the Sachs-Wolfe effect beyond the linear order. In particular, we derive the expression for the second-order CMB temperature fluctuations. The multiple scattering effect pointed out in this paper leads to the possibility that tensor metric perturbations, i.e., gravity waves, which do not exhibit gravitational instability can still contribute to the skewness in the CMB anisotropy maps. We find that in a flat $\Omega =1\mathrm{}$ universe the skewness in the CMB contributed by gravity waves via the multiple scattering effect is comparable to that from the gravitational instability of scalar perturbations for equal contributions of the gravity waves and scalar perturbations to the total rms CMB anisotropy. The secondary skewness is found to be smaller than the cosmic variance leading to the conclusion that inflationary scenarios do predict that the observed CMB anisotropy should be statistically consistent with a Gaussian random distribution.