Stochastic Backgrounds of Gravitational Waves from Cosmological Sources: Techniques and Applications to Preheating

TL;DR

This work tackles the prediction of stochastic gravitational wave backgrounds generated by classical processes in the post-inflationary universe, with a focus on preheating. It develops a robust framework based on solving the perturbed Einstein equations in the transverse-traceless gauge using exact Green's functions for radiation- and matter-dominated expansion, and derives a Weinberg-like formula for expanding spacetimes to relate the source stress-energy to the emitted GW energy. The authors implement a lattice-friendly computational approach, interfacing with LatticeEasy to evolve nonlinear scalar-field dynamics and extract the GW spectrum, and validate the method by reproducing results from prior preheating studies. The framework offers a general, scalable tool for translating early-universe GW production into today’s observables and points to observable prospects for cosmological phase transitions (e.g., electroweak-scale) with detectors such as LISA.

Abstract

Several mechanisms exist for generating a stochastic background of gravitational waves in the period following inflation. These mechanisms are generally classical in nature, with the gravitational waves being produced from inhomogeneities in the fields that populate the early universe and not quantum fluctuations. The resulting stochastic background could be accessible to next generation gravitational wave detectors. We develop a framework for computing such a background analytically and computationally. As an application of our framework, we consider the stochastic background of gravitational waves generated in a simple model of preheating.

Figures (4)

• Figure 1: Variances of $\phi$ and $\chi$ fields, as computed by LatticeEasy. Note that these units do not account for the expansion of the universe.
• Figure 2: Evolution of the scale factor as a function of time, computed by LatticeEasy. Note that, to an extremely good approximation, the evolution is completely radiation-dominated.
• Figure 3: The spectrum of the stochastic background today, $\Omega_{{\rm gw}}h^2$, computed along six directions on the lattice (thin colored lines), and the average (thick black line).
• Figure 4: Comparison of $\Omega_{\rm gw}$ today as computed by the method described in this paper (solid black line), as well as the curves published in Dufaux:2007pt (dash-dotted blue line), Easther:2007vj (dashed green line) and GarciaBellido:2007af (dotted red line). Note the good agreement across methods.