ANISOTROPIES OF THE COSMIC BACKGROUND-RADIATION IN A HOT DARK MATTER UNIVERSE

We investigate microwave photons propagating through the evolving density inhomogeneities in a model universe filled with "hot" dark matter. The evolution takes place in a comoving cube now 165 Mpc on a side, beginning at z = 1900 before the epoch of decoupling and continuing to the present time z = 0. We take the density parameter OMEGA-0 = 1 and the Hubble constant H0 = 100h km s-1 Mpc-1 with h = 1. Our calculation is fully three-dimensional and we follow the density inhomogeneities into the nonlinear regime. We have included the effect of Thomson scattering throughout the model history using a Monte Carlo scattering algorithm. The optical depth for this scattering is a function of time determined by the free electron density, which we obtain by our numerical integration of the relevant equations in our particular model universe. We display our results in the form of sky maps such as an observer might make; the maps are of 4-degrees x 4-degrees and 2-degrees x 2-degrees regions. We find structure on these scales with amplitudes 7 x 10(-6) less-than-or-equal-to (DELTA-T/T)rms less-than-or-equal-to 1.4 x 10(-5) with peak excursions DELTA-T/T approximately 3 x 10(-5), which is consistent with the best current observational limit of 4 x 10(-5) set by the COBE data at 7-degrees and 3.5 x 10(-5) set by the South Pole experiment of P. Meinhold and P. Lubin at approximately 1-degrees.