A Gravitational Wave Background from Reheating after Hybrid Inflation

TL;DR

This work analyzes the stochastic gravitational-wave background produced during reheating after hybrid inflation, focusing on three successive stages: tachyonic preheating, bubble-like collisions, and turbulence. Using a TT-projection formalism and non-perturbative lattice simulations, the authors evolve the coupled scalar-field and metric perturbation dynamics, justifying a classical approximation for the highly occupied long-wavelength modes. They find that the GW signal can be substantial for GUT-scale inflation at frequencies around 10^7–10^9 Hz, but only low-scale hybrid inflation yields signals potentially detectable by future detectors such as BBO or DECIGO, with a distinct spectral shape tied to the reheating dynamics. The study also cross-validates chaotic-inflation reheating results, reinforcing the method's applicability and highlighting the GW background as a probe of the inflationary paradigm and the physics of reheating.

Abstract

The reheating of the universe after hybrid inflation proceeds through the nucleation and subsequent collision of large concentrations of energy density in the form of bubble-like structures moving at relativistic speeds. This generates a significant fraction of energy in the form of a stochastic background of gravitational waves, whose time evolution is determined by the successive stages of reheating: First, tachyonic preheating makes the amplitude of gravity waves grow exponentially fast. Second, bubble collisions add a new burst of gravitational radiation. Third, turbulent motions finally sets the end of gravitational waves production. From then on, these waves propagate unimpeded to us. We find that the fraction of energy density today in these primordial gravitational waves could be significant for GUT-scale models of inflation, although well beyond the frequency range sensitivity of gravitational wave observatories like LIGO, LISA or BBO. However, low-scale models could still produce a detectable signal at frequencies accessible to BBO or DECIGO. For comparison, we have also computed the analogous gravitational wave background from some chaotic inflation models and obtained results similar to those found by other groups. The discovery of such a background would open a new observational window into the very early universe, where the details of the process of reheating, i.e. the Big Bang, could be explored. Moreover, it could also serve in the future as a new experimental tool for testing the Inflationary Paradigm.

Figures (18)

• Figure 1: Time evolution of the mean field values of the Higgs and the Inflaton, the former normalized to its v.e.v., the latter normalized to its critical value $\chi_{0} = \rm{m/g}$. This is just a specific realization with $N = 128$, $p_{\rm min} = 0.1m$, $a = 0.48m^{-1}$, $v = 10^{-3}M_p$ and $g^2 = 2\lambda = 0.25$.
• Figure 2: The time evolution of the different types of energy (kinetic, gradient, potential, anisotropic components and gravitational waves for different lattices), normalized to the initial vacuum energy, after hybrid inflation, for a model with $v=10^{-3}\,M_P$. One can clearly distinguish here three stages: tachyonic growth, bubble collisions and turbulence.
• Figure 3: We show here the comparison between the power spectrum of gravitational waves obtained with increasing lattice resolution, to prove the robustness of our method. The different realizations are characterized by the the minimum lattice momentum (p$_{\rm min}$) and the lattice spacing (ma). The growth is shown in steps of $m\Delta t = 1$ up to $mt = 30$, and then in and $m\Delta t = 5$ steps up to $mt = 60$.
• Figure 4: The tachyonic growth of the Higgs' spectrum, from $mt=5$ to $mt=10$. We compare simulations of different sizes ($p_{\rm min} = 0.01 - 0.03$) and $N=256$, with the anaylitical expressions.
• Figure 5: The Fourier transform of the anisotropic stress tensor. We compare the numerical simulations of $\Pi_{11}(k,t)$ for $p_{\rm min} = 0.01$ with the analytical expressions (dashed lines) for $mt=5 - 10$, i.e. during the tachyonic growth. The small deviations at $k\leq m$ are simulation artifacts due to the initial UV cut-off implementation and soon disappear.