A Statistic for the Detection of Long Strings in Microwave Background Maps

Abstract

Using analytical methods and Monte Carlo simulations, we analyze a new statistic designed to detect isolated step-like discontinuities which are coherent over large areas of Cosmic Microwave Background (CMB) pixel maps. Such coherent temperature discontinuities are predicted by the Kaiser-Stebbins effect to form due to long cosmic strings present in our present horizon. The background of the coherent step-like seed is assumed to be a scale invariant Gaussian random field which could have been produced by a superposition of seeds on smaller scales and/or by inflationary quantum fluctuations. The effects of uncorrelated Gaussian random noise are also studied. The statistical variable considered is the Sample Mean Difference (SMD) between large neighbouring sectors of CMB maps, separated by a straight line in two dimensional maps and a point in one dimensional maps. We find that including noise, the SMD statistics can detect at the $1 σ$ to $2 σ$ level the presense of a long string with $Gμ(v_s γ_s)= 1/(8π) ((δT)/T)_{rms} \simeq 0.5 \times 10^{-7}$ while more conventional statistics like the skewness or the kurtosis require a value of $Gμ$ almost an order of magnitude larger for detectability at a comparable level.