Cosmic Microwave Background Anisotropy Correlation Function and Topology from Simulated Maps forMAP

Abstract

We have simulated cosmic microwave background (CMB) anisotropy maps for several COBE-Differential Microwave Radiometer experiment normalized cold dark matter (CDM) cosmogonies, to make predictions for the MAP experiment, an upcoming whole-sky CMB anisotropy space mission. We have studied the sensitivity of the simulated MAP data to cosmology, sky coverage, and instrumental noise. Given an accurate knowledge of instrumental noise, MAP data will ably discriminate among the cosmogonies considered, and superbly determine the topology of the initial fluctuations. A correlation function analysis of the simulated MAP data results in a very accurate measurement of the acoustic Hubble radius at decoupling. A low-density open CDM model with Ω0 = 0.4 can be distinguished from the Ω0 = 1 fiducial CDM model or a spatially flat CDM model with a cosmological constant and Ω0 = 0.4 with more than 99% confidence from the location of the acoustic valley in the correlation function. A genus analysis of the simulated MAP data indicates that in cosmogonies with Gaussian random-phase initial conditions, the horizontal shift of the zero-crossing point of the genus curve near the mean temperature threshold level ν = 0 should not exceed |Δν| = 0.01 (0.04) when the total effective FWHM smoothing is 03 (10). The asymmetry of the genus curve at the positive and negative threshold levels should not exceed |Δg/g(ν = ±1)| = 0.8% (4%) at 03 (1°) FWHM smoothing. Deviations of the observed MAP data in excess of these small values will be evidence for non-Gaussian behavior. The amplitude of the genus curve is a measure of the shape of the power spectrum at the smoothing scale. Even with the expected amount of instrumental noise and partial sky coverage (due to the Galaxy), the MAP data should allow discrimination among the cosmogonies considered at more than 99% confidence solely from a genus amplitude analysis.