Scaling from gauge and scalar radiation in Abelian Higgs string networks
  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 self-similarity of the networks
over a wide range of scales, and estimate the asymptotic values of the mean
string separation in horizon length units $\dot{\xi}$ and of the mean square
string velocity $\bar v^2$ 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 compare $\dot{\xi}$ and $\bar v^2$ to values measured in
simulations using the Nambu-Goto approximation, finding that the latter
underestimate the mean string separation by about 25%, and overestimate $\bar
v^2$ 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.
