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

We have simulated cosmic microwave background (CMB) anisotropy maps forseveral COBE-DMR-normalized cold dark matter (CDM) cosmogonies, to makepredictions for the upcoming MAP experiment. We have studied the sensitivity ofthe simulated MAP data to cosmology, sky coverage, and instrumental noise. Withaccurate knowledge of instrumental noise, MAP data will discriminate among thecosmogonies considered, and determine the topology of the initial fluctuations. A correlation function analysis of the simulated MAP data results in a veryaccurate measurement of the acoustic Hubble radius at decoupling. A low-densityopen CDM model with Omega_0=0.4 can be distinguished from the Omega_0=1fiducial CDM model or a Lambda CDM model with > 99% confidence from thelocation of the acoustic "valley" in the correlation function. A genus analysis of the simulated MAP data indicates that in cosmogonies withGaussian random-phase initial conditions, a shift of the zero-crossing point ofthe genus curve near the mean temperature threshold level nu=0 should notexceed |Delta nu| = 0.01 (0.04) when the total effective FWHM smoothing is 0.3deg (1.0 deg). The asymmetry of the genus curve at the positive and negativethreshold levels should not exceed |Delta g/g(nu=1,-1)| = 0.8% (4%) at 0.3 deg(1.0 deg) FWHM smoothing. Deviations of the observed MAP data in excess ofthese small values will be evidence for non-Gaussian behavior. The amplitude of the genus curve is a measure of the shape of the powerspectrum at the smoothing scale. Even with the expected amount of instrumentalnoise and partial sky coverage (due to the Galaxy), the MAP data should allowdiscrimination amongst the cosmogonies considered at more than 99% confidencesolely from a genus amplitude analysis.