COBE versus cosmic strings. An analytical model

Abstract

We construct a simple analytical model to study the effects of cosmic strings on the microwave background radiation. Our model is based on counting random multiple impulses inflicted on photon trajectories by the string network between the time of recombination and today. We construct the temperature auto-correlation function and use it to obtain the effective power spectrum index n, the RMS-quadrupole-normalized amplitude Q RMS-PS and the RMS temperature variation smoothed on small angular scales. For the values of the scaling solution parameters obtained by Bennett and Bouchet [Phys. Rev. D 41 (1990) 2408] and Allen and Shellard [Phys. Rev. Lett. 64 (1990) 119] we obtain n=1.14±0.5, Q RMS-PS =(4.55±1.5)Gμ and ( ΔT T ) RMS =5.5Gμ . Demanding consistency of these results with the COBE data leads to Gμ = (1.7 ± 0.7) × 10 −6 (where μ is the string mass per unit length), in good agreement with direct normalizations of μ from observations.