Gravitational Waves From the End of Inflation: Computational Strategies

TL;DR

The paper develops and validates a spectral, expanding-background algorithm to compute the stochastic gravitational wave background generated during preheating after inflation, across a range of scalar-field inflationary models including quadratic, quartic, and low-scale hybrid potentials. By evolving the scalar fields on a lattice and sourcing the TT part of the stress-energy tensor to evolve metric perturbations, the authors quantify the contemporary GW spectrum and compare against alternative numerical approaches. They demonstrate consistency with previous methods, reveal model-dependent resonance differences (notably inverted-hybrid potentials), and discuss observational prospects for future detectors. The work provides a versatile framework for connecting microphysical reheating processes to detectable gravitational radiation and sets the stage for broader applications to other inhomogeneity-driven GW sources.

Abstract

Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from thermal equilibrium and could source a significant stochastic background of gravitational radiation. Here, we present a numerical algorithm for computing the contemporary power spectrum of gravity waves generated in this post-inflationary phase transition for a large class of scalar-field driven inflationary models. We explicitly calculate this spectrum for both quartic and quadratic models of chaotic inflation, and low-scale hybrid models. In particular, we consider hybrid models with an ``inverted'' potential. These models have a very short and intense period of resonance which is qualitatively different from previous examples studied in this context, but we find that they lead to a similar spectrum of gravitational radiation.

Figures (13)

• Figure 1: The Mathieu Stability/Instability chart. The imaginary part of the Mathieu critical exponent is plotted, with darker colors corresponding to a larger imaginary component. Outside the heavy black lines the exponent is real-valued, and the corresponding solutions are strictly oscillatory. The diagonal line corresponds to $A_q = 2 q$.
• Figure 2: From top to bottom: The scale factor, the variances of $\phi$ (solid) and $\chi$ (dotted), $S_{11}^{TT}$ for a mode corresponding to $|k|\approx 1.4 \times 10^8 \,{\rm Hz}$ today, and the maximum height of the gravitational wave spectrum for this mode as a function of time for $\lambda \phi^4$ inflation with $\lambda = 10^{-14}$ and $g^2/\lambda=120$.
• Figure 3: The upper plot shows the magnitude, in arbitrary units, versus rescaled time of the diagonal components, $h_{11}$ (solid), $h_{12}$ (dotted) and $h_{13}$ (dashed) for a mode corresponding to $|k|= 1.4 \times 10^8$ today for a $\lambda \phi^4$ model. The lower plot shows $k_1h_{11}(k)+k_2h_{12}(k)+k_3h_{13}(k)$, which demonstrates that perturbation is transverse via (\ref{['ttcondition']}).
• Figure 4: The upper plot shows the magnitude, in arbitrary units, versus rescaled time of the diagonal components, $h_{11}$ (solid), $h_{22}$ (dotted) and $h_{33}$ (dashed) for a mode corresponding to $|k|= 1.4 \times 10^8$ today for a $\lambda \phi^4$ model. The lower plot shows their sum.
• Figure 5: The evolution of the gravitational wave spectrum for a quartic inflation model, where $\lambda = 10^{-14}$ and $g^2/\lambda = 120$.