Scaling from gauge and scalar radiation in Abelian-Higgs string networks

Abstract

We investigate cosmic string networks in the Abelian Higgs model using data from a campaign of large-scale numerical simulations on lattices of up to 4096 3 grid points. We observe scaling or selfsimilarity of the networks over a wide range of scales, and estimate the asymptotic values of the mean string separation in horizon length unitsξ and of the mean square string velocityv 2 in the continuum and large time limits. The scaling occurs because the strings lose energy into classical radiation of the scalar and gauge fields of the Abelian Higgs model. We quantify the energy loss with a dimensionless radiative efficiency parameter, and show that it does not vary significantly with lattice spacing or string separation. This implies that the radiative energy loss underlying the scaling behaviour is not a lattice artefact, and justifies the extrapolation of measured network properties to large times for computations of cosmological perturbations. We also show that the core growth method, which increases the defect core width with time to extend the dynamic range of simulations, does not introduce significant systematic error. We compareξ andv 2 to values measured in simulations using the Nambu-Goto approximation, finding that the latter underestimate the mean string separation by about 25%, and overestimatev 2 by about 10%. The scaling of the string separation implies that string loops decay by the emission of massive radiation within a Hubble time in field theory simulations, in contrast to the Nambu-Goto scenario which neglects this energy loss mechanism. String loops surviving for only one Hubble time emit much less gravitational radiation than in the Nambu-Goto scenario, and are consequently subject to much weaker gravitational wave constraints on their tension.

Extending and calibrating the velocity dependent one-scale model for cosmic strings with one thousand field theory simulations

“…1, in which Gauss's law violations at single precision are displayed in the top panel, together with the behavior of a winding based correlation length estimator (see the next section for a description of the estimator itself). Within their statistical uncertainties, and for the radiation and matter era (the only cases where such a comparison is possible), our results are consistent with the measured values of [11] for the same timestep range (for a comparison see [26]), and also with the ones that can visually inferred from Figure 8 of [18], which has values directly measured in their simulations. Our results are not compatible with the ones listed in Table IX of [18] but we emphasize that those correspond to extrapolations to zero radii strings, and would therefore be appropriate for comparison with Goto-Nambu simulations but not with our work.…”

“…We do emphasize that, to the extent that a compar-ison can be made, the numerical results of our code [26] are fully consistent with those of [11,18], though our interpretation of them, which is illuminated by the physical content of the VOS model, is slightly different. One point to bear in mind, regarding the perceived differences between the results of Goto-Nambu and field theory simulations of cosmic strings is that both the physical content and the numerical diagnostics differ in subtle ways.…”

“…For this work, we will not use the field-based velocity estimator. The reason for this is that this estimator seems to systematically underestimate the velocity, which can also be seen in [18] when comparing to an oscillating string in flat space. The underestimation manifests itself in all expansion rates as seen in Fig.…”

“…For the < v 2 > estimators there are also two options. The first one comes from [16,18] and is based on the fact that for the conjugate scalar field momentum, Π, the configuration for a moving string can be given Lorentz boosts of the static field configuration. A detailed derivation can be found in [18].…”

“…and W is a weight function, meant to merely localize the estimators around strings; we will refer to this as the field-based velocity estimator. The second possibility is to use the equation of state estimator of [18], in which the volume averages of the pressure and the density (each weighted by some weight function W) then yield…”