Analytical Scaling Solutions for the Evolution of Cosmic Domain Walls in a Parameter-Free Velocity-Dependent One-Scale Model

We derive an analytical approximation for the linear scaling evolution of the characteristic length L and the root-mean-squared velocity σv of standard frictionless domain wall networks in Friedmann-Lemaître-Robertson-Walker universes with a power law evolution of the scale factor a with the cosmic time t (a∝tλ). This approximation, obtained using a recently proposed parameter-free velocity-dependent one-scale model for domain walls, reproduces well the model predictions for λ close to unity, becoming exact in the λ→1- limit. We use this approximation, in combination with the exact results found for λ=0, to obtain a fit to the model predictions valid for λ∈[0,1] with a maximum error of the order of 1%. This fit is also in good agreement with the results of field theory numerical simulations, especially for λ∈[0.9,1]. Finally, we explicitly show that the phenomenological energy-loss parameter of the original velocity-dependent one-scale model for domain walls vanishes in the λ→1- limit and discuss the implications of this result.