Loop decay in Abelian-Higgs string networks

Abstract

We study the decay of cosmic string loops in the Abelian-Higgs model. We confirm earlier results that loops formed by intersections of infinite strings formed from random-field initial conditions disappear quickly, with lifetime proportional to their initial rest-frame length l_init. We study a population with l_init up to 6000 inverse mass units, and measure the proportionality constant to be 0.14 ± 0.04, independently of the initial lengths. We propose a new method to construct oscillating non-self intersecting loops from initially stationary strings, and show that by contrast these loops have lifetimes scaling approximately as l^2_init, in line with previous works on artificially created string configurations. We show that the oscillating strings have mean-square velocity v ̄2=0.500 ± 0.004, consistent with the Nambu-Goto value of 1/2, while the network loops have v ̄2=0.40 ± 0.04. We argue that whatever the mechanism behind the network loop decay is, it is non-linear, can only be suppressed by careful tuning of initial conditions, and is much stronger than gravitational radiation. An implication is that one cannot use the Nambu-Goto model to derive robust constraints on the tension of field theory strings. We advocate parametrising the uncertainty as the fraction fNG of Nambu-Goto-like loops surviving to radiate gravitationally. None of the 31 large network loops created survived longer than 0.25 of their initial length, so one can estimate that fNG < 0.1 at 95% confidence level. If the recently reported NANOgrav signal is due to cosmic strings, fNG must be greater than 10^-3 in order not to violate bounds from the Cosmic Microwave Background.