Production of Gravitational Waves from Preheating and Tachyonic Instabilities

TL;DR

This paper investigates gravitational wave production during preheating in an alpha-attractor inflation model terminated in the positive-curvature regime, incorporating a trilinear coupling h phi chi^2. Using both Floquet analysis and 3D lattice simulations, it shows that inflaton fluctuations undergo parametric resonance while chi experiences tachyonic bursts, producing a stochastic GW background with a characteristic double-peak spectrum. After redshifting, the present-day GW signal features a dominant peak at f_p^(0) ~ 10^7 Hz with h^2 Omega_GW^(0) ~ 10^-11, a signature of multi-channel preheating in these models. Although current detectors cannot access such ultra-high frequencies, future MHz–GHz experiments may probe this early-universe epoch, offering a window into post-inflationary dynamics and energy transfer mechanisms.

Abstract

We analyze GW production during preheating for an $α$-attractor potential terminating in the positive-curvature regime, with energy transfer via $φχ^{2}$. Linear Floquet analysis and nonlinear simulations show that $φ$ fluctuations grow by parametric resonance, while $χ$ undergoes tachyonic bursts. The GW spectrum features two peaks: a dominant low-frequency peak from the parametric channel and a subdominant high-frequency peak from the tachyonic channel. Redshifted to today, the peak reaches $h^{2}Ω_{\rm GW}^{(0)} \sim 10^{-11}$ at $f^{(0)}_{p} \sim 10^{7}$ Hz. This multi-peak structure is a characteristic imprint of trilinear preheating in $α$-attractors.

Figures (10)

• Figure 1: The field value at the inflection point (red dashed line) and the field value at the end of inflation (black solid line) are shown as functions of $M$ in units of $M_{\rm pl} = 1$. The shaded region denotes the domain of positive curvature in the potential.
• Figure 2: The time evolution of the spatially averaged inflaton field, $\langle \tilde{\phi} \rangle$, and the daughter field, $\langle \tilde{\chi} \rangle$, is shown.
• Figure 3: In the left panel, the time evolution of the inflaton field fluctuation, $\delta \tilde{\phi}_{\tilde{k}}$, for different modes $\tilde{k}$ is depicted by solving Eq. \ref{['phi_k_eq']}. In the right panel, the evolution of $\delta \tilde{\phi}_{\tilde{k}}$ for the resonant mode $\tilde{k}_{\rm res} = 2.04$ is displayed: (i) obtained by solving Eq. \ref{['phi_k_eq']} (red line) and (ii) computed using CosmoLattice (blue line).
• Figure 4: In the left panel, the time evolution of $q_3 \tilde{\phi}_0$ (blue) and $3 q_4 \langle \tilde{\chi}^2 \rangle$ (black) is depicted. The blue dashed segments indicate intervals during which the inflaton field $\tilde{\phi}_0$ takes negative values. The growth of the fluctuation for a given mode $\tilde{k}$ is illustrated by the red dashed line. In the right panel, the blue and black curves represent the occupation number of the daughter field obtained analytically, $n_{\tilde{k}, \tilde{\chi}} \propto e^{\tilde{\eta}^{3/2}}$Abolhasani:2010, and from lattice simulations, respectively. The red solid and red dashed curves denote the effective frequency $\tilde{\omega}_{\tilde{k}, \tilde{\chi}}^2$ with and without backreaction effects, respectively. For both panels, the parameters $\tilde{k} = 1.2$, $q_3 = 100$, and $q_{\chi} = 2 \times 10^{10}$ are used.
• Figure 5: In the left panel, the power spectrum of the inflaton field $\tilde{\phi}$ is displayed. In the right panel, the power spectrum of the daughter field $\tilde{\chi}$ is shown.