Gravitational waves from cosmic strings for pedestrians

TL;DR

This paper derives analytical formulas for gravitational wave spectra from cosmic strings, enabling efficient and accurate predictions across all frequencies and tensions, improving upon previous numerical methods.

Contribution

It provides a novel, fully analytical derivation of the GW spectrum from cosmic strings using the Nambu-Goto approximation and velocity-dependent one-scale model, valid over the entire parameter space.

Findings

Analytical expressions for GW spectra valid across all frequencies.

Formulas account for cosmic string tension and frequency spectrum.

Discussion of spectral features and effects of cosmological parameters.

Abstract

Cosmic strings represent an attractive source of gravitational waves (GWs) from the early Universe. However, numerical computation of the GW signal from cosmic strings requires the evaluation of complicated integral and sum expressions, which can become computationally costly in large parameter scans. This motivates us to rederive the GW signal from a network of local stable cosmic strings in the Nambu-Goto approximation and based on the velocity-dependent one-scale model from a ``pedestrian'' perspective. That is, we derive purely analytical expressions for the total GW spectrum, which remain exact wherever possible and whose error can be tracked and reduced in a controlled way in crucial situations in which we are forced to introduce approximations. In this way, we obtain powerful formulas that, unlike existing results in the literature, are valid across the entire frequency spectrum and across the entire conceivable range of cosmic-string tensions. We provide an in-depth discussion of the GW spectra thus obtained, including their characteristic break frequencies and approximate power-law behaviors, comment on the effect of changes in the effective number of degrees of freedom during radiation domination, and conclude with a concise summary of our main formulas that can readily be used in future studies.