Gravitational Waves from Abelian Gauge Fields and Cosmic Strings at Preheating

TL;DR

This work develops a theoretical and numerical framework to quantify gravitational waves produced by out-of-equilibrium Abelian gauge fields during preheating after hybrid inflation. By embedding the Abelian-Higgs model in a lattice-GW calculation, the authors reveal that gauge-field dynamics imprint multiple characteristic peaks in the GW spectrum and tie these features to the formation and evolution of Nielsen-Olesen strings. The study demonstrates, through detailed Fourier and configuration-space analyses, how Higgs bubbles collide and magnetic flux tubes form and evolve, driving GW production that eventually saturates in a turbulent regime. The results show promising connections between preheating microphysics, topological defects, and observable GW signatures, and they outline extensions to non-Abelian theories and potential implications for upcoming GW observatories.

Abstract

Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at preheating. We then consider models of preheating after hybrid inflation, where the symmetry breaking field is charged under a local U(1) symmetry. We analyze in detail the dynamics of the system in both momentum and configuration space, and show that gauge fields leave specific imprints in the resulting gravitational wave spectra, mainly through the appearence of new peaks at characteristic frequencies that are related to the mass scales in the problem. We also show how these new features in the spectra correlate with string-like spatial configurations in both the Higgs and gauge fields that arise due to the appearance of topological winding numbers of the Higgs around Nielsen-Olesen strings. We study in detail the time evolution of the spectrum of gauge fields and gravitational waves as these strings evolve and decay before entering a turbulent regime where the gravitational wave energy density saturates.

Figures (15)

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• Figure 3: Contribution of different source terms to GW production from wave-like fields. Left pannel: contribution associated to the source term in $\partial_i \phi \partial_j \phi$ for scalar fields, corresponding to the interaction between two scalar waves and a graviton (forbidden by helicity conservation). Middle pannel: contribution associated to the terms in (\ref{['AAh']}), corresponding to the interaction between two vector waves and a graviton (allowed if the vector field is massless). Right pannel: contribution associated to the second term in (\ref{['AAXXh']}), corresponding to the interaction between several scalar and vector waves and a graviton.
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