CBR anisotropy from primordial gravitational waves in inflationary cosmologies

Abstract

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. These temperature fluctuations are described by an angular correlation function $C(γ)$. A new (more concise and general) derivation of $C(γ)$ is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles $γ$ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode functions. The function $C(γ)$ may be expanded in a series of Legendre polynomials; we use numerical methods to compare the coefficients of the resulting expansion in our exact calculation with standard (approximate) results. We also report some progress towards finding a closed form expression for $C(γ)$.