Spectral Analysis of Microwave Background Perturbations Induced by Cosmic Strings

Using a simple analytic model based on seed superposition we obtain the spectrum of microwave background perturbations induced by cosmic strings on all angular scales larger than about 2 armin. We assume standard recombination in an Einstein de Sitter universe with $h=1/2$ and study the fluctuation spectrum along a great circle in the sky. Doppler and potential perturbations on the last scattering surface (Sachs-Wolfe effect) are shown to dominate over post-recombination perturbations on scales smaller than about 2 degrees. Using a filter function corresponding to the COBE experiment we obtain an effective power spectrum index $n_{eff}\simeq 1.35$ in good agreement with the recently announced second year COBE data showing $n_{eff}\simeq 1.5$. The only free parameter ($G\mu$) of the string model is fixed by normalizing on the COBE detection leading to $G\mu=1.6$. Other parameters (e.g. the {\it rms} string velocity) are fixed by comparing with string simulations. Using these parameter values we compare the {\it rms} temperature fluctuations $({{\Delta T}\over T})_{\it rms}$ predicted for ongoing experiments (Tenerife, SP91, MAX, OVRO etc) with detections and with the corresponding predictions of inflationary models.