Physical and invariant models for defect network evolution

Understand

We revisit the velocity-dependent one-scale model for topological defect evolution, and present a new alternative formulation in terms of a physical (rather than invariant) characteristic length scale.

• While the two approaches are equivalent (as we explicitly demonstrate), the new one is particularly relevant when studying the evolution of ultra-relativistic defects.
• Moreover, a comparison of the two provides further insight on the interpretation of the model's two phenomenological parameters, $c$ related to energy losses and $k$ related to the curvature of the defects.
• As an illustration of the relevance of the new formulation, we use it to study the evolution of cosmic string and domain wall networks in contracting universes.