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Register a new userParameter-free velocity-dependent one-scale model for domain walls
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P. P. Avelino
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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.
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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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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.
We study the evolution of cosmological domain walls in models with asymmetric potentials. Our research goes beyond the standard case of spontaneous breaking of an approximate symmetry. When the symmetry is explicitly broken the potential exhibits nearly degenerate minima which can lead to creation of a metastable network of domain walls. The time after which the network will decay depends on the difference of values of the potential in minima, its asymmetry around the maximum separating minima and the bias of initial distribution. Using numerical lattice simulations we determine relative importance of these factors on decay time of networks for generic potentials. We find that even very small departures from the symmetric case lead to rapid decay of the domain wall network. As a result creation of a long lasting network capable of producing observable gravitational wave signals is much more difficult than previously thought.
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