On the Number of Cosmic Strings
  The number of cosmic strings in the observable universe is relevant in determining the probability of detecting such cosmic defects through their gravitational signatures. In particular, we refer to the observation of gravitational lensing events and anisotropy in the CMB radiation induced by cosmic strings. In this paper, a simple method is adopted to obtain an approximate estimate of the number of segments of cosmic strings, crossing the particle horizon, which fall inside the observed part of the universe. We show that there is an appreciable difference in the expected number of segments which differentiates cosmic strings arising in Abelian Higgs and Nambu-Goto models, and that a different choice of setting for the cosmological model can lead to significant differences in the expected number of cosmic string segments. Of this number, the fraction realistically detectable may be considerably smaller. 
Rosa Consiglio, Olga Sazhina, Giuseppe Longo, Mikhail Sazhin, Franco   Pezzella
astro-ph.CO