Cosmic Strings & Cosmic Variance

By using a simple analytical model based on counting random multiple impulses inflicted on photons by a network of cosmic strings we show how to construct the general q-point temperature correlation function of the Cosmic Microwave Background radiation. Our analysis is sensible specially for large angular scales where the Kaiser-Stebbins effect is dominant. Then we concentrate our study on the four-point function and in particular on its zero-lag limit, namely, the excess kurtosis parameter, for which we obtain a predicted value of ∼ 10. In addition, we estimate the cosmic variance for the kurtosis due to a Gaussian fluctuation field, showing its dependence on the primordial spectral index of density fluctuations n and finding agreement with previous published results for the particular case of a flat HarrisonZel’dovich spectrum. Our value for the kurtosis compares well with previous analyses but falls below the threshold imposed by the cosmic variance when commonly accepted parameters from string simulations are considered. In particular the non-Gaussian signal is found to be inversely proportional to the scaling number of defects, as could be expected by the central limit theorem. Subject headings: cosmic microwave background cosmic strings Electronic mail: [email protected] Electronic mail: [email protected] Address after September 1, 1994: Department of Physics, M.I.T., Cambridge, MA 02139