Probabilistic estimates of the number of cosmic strings

The dependences of the mean expected number of cosmic strings on their redshift up to the surface of last scattering have been derived. The calculations are based on the geometric probability of a straight string segment crossing a given field and on information about the absence of strings when they are searched for via their gravitational lensing effects in optical catalogs. It is shown that there are no strings for redshifts 0 < z < 1.954, but the expected number of strings for 0 < z < 5 can be no more than 2.1 × 10³ at the 95% confidence level. The expected number of strings for redshifts up to z = 1100 can be no more than 2.4 × 10⁴ at the 95% confidence level. The latter estimate is sensitive to a priori information about the absence of cosmic strings in the redshift range 0 < z < 1.954 in a field of 4.48 square degrees in optical catalogs; it is smaller than the estimate without allowance for this information by 6%.