# Cosmic strings and other topological defects in nonscaling regimes

## TL;DR

This paper uses an improved analytical model to study the evolution of cosmic string networks across different cosmic epochs, accounting for realistic cosmological conditions and dark energy effects.

## Contribution

It introduces new approximate solutions for cosmic string network behavior during key cosmological transitions, moving beyond the simplistic scaling assumption.

## Key findings

- Derived analytic solutions for radiation-to-matter transition
- Derived analytic solutions for matter-to-acceleration transition
- Numerically analyzed string network properties for various dark energy models

## Abstract

Cosmic strings are topological defects possibly formed in the early Universe, which may be observable due to their gravitational effects on the cosmic microwave background radiation or gravitational wave experiments. To this effect it is important to quantitatively ascertain the network properties, including their density, velocity or the number of strings present, at the various epochs in the observable Universe. Attempts to estimate these numbers often rely on simplistic approximations for the string parameters, such as assuming that the network is scaling. However, in cosmological models containing realistic amounts of radiation, matter and dark energy a string network is never exactly scaling. Here we use the velocity-dependent one-scale model for the evolution of a string network to better quantify how these networks evolve. In particular we obtain new approximate analytic solutions for the behavior of the network during the radiation-to-matter and matter-to-acceleration transitions (assuming, in the latter case, the canonical $\Lambda$ cold dark matter model), and numerically calculate the relevant quantities for a range of possible dark energy models.