Gravity Waves from Tachyonic Preheating after Hybrid Inflation

TL;DR

This work analyzes the stochastic gravitational wave background produced by tachyonic preheating after hybrid inflation. It combines analytic estimates and lattice simulations to map how the GW spectrum depends on the model parameters $\lambda$, $g$, $v$, and the initial inflaton velocity $V_c$, across three dynamical regimes. The study derives scaling relations for the GW peak frequency $f_*$ and peak energy density $h^2\Omega^*_{gw}$ in each regime and demonstrates that observable GW signals in interferometers like Advanced LIGO require extremely small couplings, highlighting tight constraints on hybrid inflation scenarios. The results illuminate how post-inflationary dynamics imprint detectable gravitational waves, offering a potential probe of early-universe physics under specific parameter conditions.

Abstract

We study the stochastic background of gravitational waves produced from preheating in hybrid inflation models. We investigate different dynamical regimes of preheating in these models and we compute the resulting gravity wave spectra using analytical estimates and numerical simulations. We discuss the dependence of the gravity wave frequencies and amplitudes on the various potential parameters. We find that large regions of the parameter space leads to gravity waves that may be observable in upcoming interferometric experiments, including Advanced LIGO, but this generally requires very small coupling constants.

Figures (14)

• Figure 1: Hybrid inflation potential. The left panel shows the potential as a function of the fields $\phi$ and $\sigma$. Only one direction of $\sigma$ is shown. The red dots (on the ridge) show the critical (bifurcation) points and the green dots (in the valleys) show the minima. The inflaton velocity after inflation moves it along the top of the ridge. For $g^2 << \lambda$ with a small initial velocity the fields roll along the indicated ellipse, as can be seen in the field histograms in the right panel.
• Figure 2: The left and middle panels show the evolution with time of the inflaton's mean normalized to $\phi_c$ (blue), $\langle\phi / \phi_c\rangle$, and of the mean of the Higgs modulus normalized to its vev (red), $\langle|\sigma|/v\rangle$ (where $|\sigma|^2 = \sigma_1^2 + \sigma_2^2$), for $\lambda / g^2 = 0.5$ (left panel) and $\lambda / g^2 = 2000$ (middle panel). The other parameters are $V_c = 10^{-3}$ and $\lambda = 10^{-5}$ in both cases. The right panel shows the evolution with time of the variances $\mathrm{Log}[\langle\delta \phi^2 / \phi_c^2\rangle]$ (blue) and $\mathrm{Log}[\langle\delta \sigma^2 / v^2\rangle]$ (red) for the case $\lambda / g^2 = 2000\,$.
• Figure 3: Field amplitude and gravity wave density as a function of space on a two dimensional slice through the lattice. The slice is chosen at the height where the first Higgs bubble appeared. The simulation is of the model (\ref{['hybrid']}) with $\lambda=10^{-5}$, $\lambda/g^2=0.5$, $v=10^{-3}$, and $V_c=0$.
• Figure 4: Gravity wave spectra for the model (\ref{['hybrid']}) with $\lambda=10^{-14}$, $\lambda/g^2=0.5$, $v=10^{-3}$, and $V_c=10^{-5}$. Lower (red) curves correspond to earlier moments of the simulation and higher (bluer) curves are from later moments of the simulation. All results are scaled to the present-day spectrum.
• Figure 5: Dependence of GW final spectra on $V_c$. The curves from left to right correspond to $V_c=10^{-5}$, $V_c=10^{-4}$, $V_c=10^{-3}$, and $V_c=10^{-2}$. Here $\lambda=10^{-14}$.