Topology of microwave background fluctuations - Theory

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Abstract

Topological measures are used to characterize the microwave background temperature fluctuations produced by "standard" scenarios (Gaussian) and by cosmic strings (non-Gaussian). Three topological quantities: total area of the excursion regions, total length, and total curvature (genus) of the isotemperature contours, are studied for simulated Gaussian microwave background anisotropy maps and then compared with those of the non-Gaussian anisotropy pattern produced by cosmic strings. In general, the temperature gradient field shows the non-Gaussian behavior of the string map more distinctively than the temperature field for all topology measures. The total contour length and the genus are found to be more sensitive to the existence of a stringy pattern than the usual temperature histogram. Situations when instrumental noise is superposed on the map, are considered to find the critical signal-to-noise ratio for which strings can be detected. With current observational sensitivity (5 mK Hz-^1/2^) and a 32 receiver array, 660 hr of mapping would demonstrate the non-Gaussian behavior due to cosmic strings if Gμ > 6 x 10^-6^. If such an observational program failed to detect any signals beyond instrumental noise, using our topological analysis we would be able to set limits of Gμ < x 10^7^ for strings and <a^2^_2_>^1/2^ <= 8 X 10^-7^ for the Zel'dovich spectrum.

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