Gravitational waves from self-ordering scalar fields

TL;DR

This work investigates gravitational waves produced by self-ordering scalar fields with global ${\rm O}(N)$ symmetry on superhorizon scales after a phase transition or preheating. Using a large-$N$ non-linear sigma-model, it derives totally coherent unequal-time correlators for the Goldstone sector and computes the resulting GW spectrum via the TT anisotropic stress source and Green-function evolution in a radiation-dominated Universe. It identifies two regimes: short-lived sources yield a strongly blue, highly suppressed IR spectrum, whereas long-lived sources produce a scale-invariant background with amplitude set by $(v/M_{\rm Pl})^4$; for GUT-scale $v$ this background could be detectable by future experiments like BBO and, in some parameter regions, marginally by LIGO/LISA. The results imply that a self-ordering GW background can compete with those from inflation, and distinguishing them may require complementary information about the underlying physics. Overall, the paper provides analytic and numerical predictions for IR GW signatures from self-ordering fields and connects them to current and future GW observatories.

Abstract

Gravitational waves were copiously produced in the early Universe whenever the processes taking place were sufficiently violent. The spectra of several of these gravitational wave backgrounds on subhorizon scales have been extensively studied in the literature. In this paper we analyze the shape and amplitude of the gravitational wave spectrum on scales which are superhorizon at the time of production. Such gravitational waves are expected from the self ordering of randomly oriented scalar fields which can be present during a thermal phase transition or during preheating after hybrid inflation. We find that, if the gravitational wave source acts only during a small fraction of the Hubble time, the gravitational wave spectrum at frequencies lower than the expansion rate at the time of production behaves as $Ω_{\rm GW}(f) \propto f^3$ with an amplitude much too small to be observable by gravitational wave observatories like LIGO, LISA or BBO. On the other hand, if the source is active for a much longer time, until a given mode which is initially superhorizon ($kη_* \ll 1$), enters the horizon, for $kη\gtrsim 1$, we find that the gravitational wave energy density is frequency independent, i.e. scale invariant. Moreover, its amplitude for a GUT scale scenario turns out to be within the range and sensitivity of BBO and marginally detectable by LIGO and LISA. This new gravitational wave background can compete with the one generated during inflation, and distinguishing both may require extra information.