Cosmic strings and other topological defects in nonscaling regimes
  Cosmic strings are topological defects possibly formed in the early Universe,
which may be observable due to their gravitational effects on the cosmic
microwave background radiation or gravitational wave experiments. To this
effect it is important to quantitatively ascertain the network properties,
including their density, velocity or the number of strings present, at the
various epochs in the observable Universe. Attempts to estimate these numbers
often rely on simplistic approximations for the string parameters, such as
assuming that the network is scaling. However, in cosmological models
containing realistic amounts of radiation, matter and dark energy a string
network is never exactly scaling. Here we use the velocity-dependent one-scale
model for the evolution of a string network to better quantify how these
networks evolve. In particular we obtain new approximate analytic solutions for
the behavior of the network during the radiation-to-matter and
matter-to-acceleration transitions (assuming, in the latter case, the canonical
$\Lambda$ cold dark matter model), and numerically calculate the relevant
quantities for a range of possible dark energy models.
