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 lifetimes proportional to their initial rest-frame length, ${\ensuremath{\ell}}_{\mathrm{init}}$. We study a population with ${\ensuremath{\ell}}_{\mathrm{init}}$ up to 6000 inverse mass units and measure the proportionality constant to be $0.14\ifmmode\pm\else\textpm\fi{}0.04$, independently of the initial lengths. We propose a new method to construct oscillating nonself intersecting loops from initially stationary strings and show that by contrast these loops have lifetimes scaling approximately as ${\ensuremath{\ell}}_{\mathrm{init}}^{2}$, in line with previous works on artificially created string configurations. We show that the oscillating strings have a mean-square velocity of ${\overline{v}}^{2}\ensuremath{\simeq}0.500\ifmmode\pm\else\textpm\fi{}0.004$, consistent with the Nambu-Goto value of $1/2$, while the network loops have ${\overline{v}}^{2}\ensuremath{\simeq}0.40\ifmmode\pm\else\textpm\fi{}0.04$. We argue that whatever the mechanism behind the network loop decay is, it is nonlinear, 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 parametrizing the uncertainty as the fraction ${f}_{\mathrm{NG}}$ 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 ${f}_{\mathrm{NG}}<0.1$ at 95% confidence level. If the recently reported NANOgrav signal is due to cosmic strings, ${f}_{\mathrm{NG}}$ must be greater than ${10}^{\ensuremath{-}3}$ in order not to violate bounds from the cosmic microwave background.