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We apply a recently developed formalism to study the evolution of a current-carrying string network under the simple but generic assumption of a linear equation of state. We demonstrate that the existence of a scaling solution with non-trivial current depends on the expansion rate of the universe, the initial root mean square current on the string, and the available energy loss mechanisms. We find that the fast expansion rate after radiation-matter equality will tend to rapidly dilute any pre-existing current and the network will evolve towards the standard Nambu-Goto scaling solution (provided there are no external current-generating mechanisms). During the radiation era, current growth is possible provided the initial conditions for the network generate a relatively large current and/or there is significant early string damping. The network can then achieve scaling with a stable non-trivial current, assuming large currents will be regulated by some leakage mechanism. The potential existence of current-carrying string networks in the radiation era, unlike the standard Nambu-Goto networks expected in the matter era, could have interesting phenomenological consequences.
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We develop a parameter-free velocity-dependent one-scale model for the evolution of the characteristic length $L$ and root-mean-square velocity $sigma_v$ of standard domain wall networks in homogeneous and isotropic cosmologies. We compare the frictionless scaling solutions predicted by our model, in the context of cosmological models having a power law evolution of the scale factor $a$ as a function of the cosmic time $t$ ($a propto t^lambda$, $0< lambda < 1$), with the corresponding results obtained using field theory numerical simulations. We show that they agree well (within a few $%$) for root-mean-square velocities $sigma_v$ smaller than $0.2 , c$ ($lambda ge 0.9$), where $c$ is the speed of light in vacuum, but significant discrepancies occur for larger values of $sigma_v$ (smaller values of $lambda$). We identify problems with the determination of $L$ and $sigma_v$ from numerical field theory simulations which might potentially be responsible for these discrepancies.
We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string worldsheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or alternatively the string correlation length) and the root mean square (RMS) velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.
The dynamics of string junctions and their influence on the evolution of cosmic superstring networks are studied in full detail. We review kinematic constraints for colliding strings in a Friedmann-Lema^itre-Robertson-Walker background and obtain the average distribution of possible string configurations after string collisions. The study of small-scale structure enables us to investigate the average growth/reduction rate of string junctions for a given cosmic string network. Incorporating the averaged junction dynamics into the velocity-dependent one-scale model for multi-tension string networks, we improve the semi-analytic description and quantitative understanding of cosmic superstring network evolution.
We report on an extensive study of the evolution of domain wall networks in Friedmann-Lema^{i}tre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These simulations were done in $4096^3$ boxes and for a range of different fixed expansion rates, as well as for the transition between the radiation and matter eras. A detailed comparison with the velocity-dependent one-scale (VOS) model shows that this cannot accurately reproduce the results of the entire range of simulated regimes if one assumes that the phenomenological energy loss and momentum parameters are constants. We therefore discuss how a more accurate modeling of these parameters can be done, specifically by introducing an additional mechanism of energy loss (scalar radiation, which is particularly relevant for regimes with relatively little damping) and a modified momentum parameter which is a function of velocity (in analogy to what was previously done for cosmic strings). We finally show that this extended model, appropriately calibrated, provides an accurate fit to our simulations.
We perform a detailed comparison between a recently proposed parameter-free velocity-dependent one-scale model and the standard parametric model for the cosmological evolution of domain wall networks. We find that the latter overestimates the damping of the wall motion due to the Hubble expansion and neglects the direct impact of wall decay on the evolution of the root-mean-square velocity of the network. We show that these effects are significant but may be absorbed into a redefinition of the momentum parameter. We also discuss the implications of these findings for cosmic strings. We compute the energy loss and momentum parameters of the standard parametric model for cosmological domain wall evolution using our non-parametric velocity-dependent one-scale model in the context of cosmological models having a power law evolution of the scale factor $a$ with the cosmic time $t$ ($a propto t^lambda$, $0 < lambda < 1$), and compare with the results obtained from numerical field theory simulations. We further provide simple linear functions which roughly approximate the dependence of the energy loss and momentum parameters on $lambda$.
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