Analytical Scaling Solutions for the Evolution of Cosmic Domain Walls in a ParameterFree VelocityDependent OneScale Model
Abstract
We derive an analytical approximation for the linear scaling evolution of the characteristic length L and the rootmeansquared 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 parameterfree velocitydependent onescale 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 energyloss parameter of the original velocitydependent onescale model for domain walls vanishes in the λ→1‑ limit and discuss the implications of this result.
 Publication:

Symmetry
 Pub Date:
 August 2022
 DOI:
 10.3390/sym14091799
 arXiv:
 arXiv:2203.16173
 Bibcode:
 2022Symm...14.1799A
 Keywords:

 domain walls;
 parameterfree model;
 cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 9 pages