Cosmic strings as random walks

Details Cosmic strings as random walks Cosmic strings as random walks

Jun 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..33.3556s&link_type=abstract

Physical Review D (Particles and Fields), Volume 33, Issue 12, 15 June 1986, pp.3556-3559

Physics

39

Particle-Theory And Field-Theory Models Of The Early Universe, Origin And Formation Of The Universe

Scientific paper

We present a random-walk model for the formation of cosmic strings in the early Universe. Analytic results are given for the scaling of string length with straight-line end-to-end separation, the length distribution of closed loops, and the fraction of total string length in infinite strings. We explain why the string network has the statistical properties of a set of Brownian, rather than self-avoiding, random walks, even in models in which string intersections in the initial configuration are impossible. It is found that the number of closed loops per unit volume with length between l and l+dl is dn=Cξ-3/2l-5/2dl, while the scaling of the straight-line distance R between two points on a string separated by a length l is R~(lξ)1/2. The fraction of string length in infinite strings is >~(2/3)-(3/4). These results are in reasonable agreement with previous Monte Carlo simulations and are confirmed by our own computer simulations in which string intersections in the initial configuration do not occur. The prevalence of infinite strings is a natural feature in the random-walk model.

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