Quantitative string evolution

Abstract

An analytic model of long string network evolution, recently developed by the authors, is presented in detail, and modified to describe string loop evolution. By treating the average string velocity, as well as the characteristic length scale, as dynamical variables, one can include the effects of frictional forces on the evolution of the network. This generalized ''one-scale'' model provides a quantitative picture of the complete evolution of a string network, including the prediction of previously unknown transient scaling regimes and a detailed analysis of the evolution of the loop population. The evolution of all cosmologically interesting string networks is studied in detail, and possible consequences of our results are discussed. ͓S0556-2821͑96͒05516-6͔

Topological defects: A problem for cyclic universes?

“…This latter equation coincides with the averaged evolution equation for R, obtained in the context of the velocity-dependent one-scale model [12,13,39], while for the averaged velocity equation this model yields…”

“…Both the analytic [11,12,13,39,40,41,42,43] and the numerical [15,16,17] tools which we shall use rely on previous work by some of the present authors. In what follows we will limit ourselves to describing the features that are directly relevant for our analysis.…”

“…Although realistic loops chopped off by the network are of course highly irregular (and, crucially, have a considerable amount of small-scale 'wiggles' [15,16,43]), the circular solution is still a useful starting point and can provide some intuition for things to come [39]. In this example we will assume for simplicity that the universe is spatially flat and that there is a negative cosmological constant which makes the universe collapse.…”

“…Two different but complementary approaches are available to study the evolution of a cosmic string network: one can resort to large numerical simulations [14,15,16] (which are intrinsically difficult and time consuming, as one is dealing with highly non-linear objects), or one can develop analytic tools [9,11,12,13,39,43] which provide an averaged (or 'thermodynamical') description of the basic properties of the network. In what follows we shall briefly describe the best motivated of these analytic models, the velocity-dependent one-scale (VOS) model [11,12,13,39], and try to use it to deduce the basic properties of a cosmic string network during a phase of contraction.…”

Estimating the weak-lensing rotation signal in radio cosmic shear surveys

“…For our spectra, we follow the socalled velocity-dependent one-scale model (e.g. Martins & Shellard 1996. In this model a cosmic string network is characterised by a correlation length, ξ = 1/(Hγs) (where H here is the Hubble factor), and a root-mean square velocity, vrms.…”