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

Abstract

A new statistic is briefly reviewed, designed to detect isolated coherent step-like discontinuities produced by cosmic strings present at late times. As a background I superpose a scale invariant Gaussian random field which could have been produced by a superposition of seeds on all scales and/or by inflationary quantum fluctuations. The statistical variable considered is the Sample Mean Difference (SMD) between large neighbouring sectors of CMB maps, separated by lines in two dimensional maps and points in one dimensional maps. I find that the SMD statistics can detect at the $1σ$ level the presense of a long string with $Gμ(v_s γ_s)={1\over {8π}}({{δT}\over T})_{rms} \simeq 0.5 \times 10^{-7}$ 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.