Stochastic gravitational wave from graviton bremsstrahlung in inflaton decay into massive spin 3/2 particles

TL;DR

This work studies stochastic gravitational waves produced during reheating from graviton bremsstrahlung accompanying inflaton decay to massive spin-$\tfrac{3}{2}$ (Rarita–Schwinger) particles. Treating the inflaton as a homogeneous classical field with a near-minimum potential $V(\phi)\sim \phi^k$, the authors compute two-body $\phi\to \psi_\mu\psi^\mu$ and three-body $\phi\to \psi_\mu\psi^\mu h_{\mu\nu}$ decays for two non-interfering operators $\lambda_s\bar{\psi}_\mu\psi^\mu\phi$ and $\lambda_p\bar{\psi}_\mu\gamma_5\psi^\mu\phi$, expressing the rates as sums over the inflaton harmonics $n$ with weights $b_n$. The reheating dynamics are solved numerically via Boltzmann equations for $\rho_\phi$ and $\rho_R$, including the harmonic decay channels, to obtain the present GW spectrum from $d\rho_{gw}/d\ln E_w$ and its redshift to $\Omega_{gw,0}$. The resulting spectra exhibit multi-peak structures tied to the harmonic content and the potential index $k$, and while the signals are below current and planned detector sensitivities, the study demonstrates how high-frequency GWs can encode inflationary microphysics and RS-sector parameters, offering a pathway to probe reheating if detector capabilities improve.

Abstract

The detection of primordial gravitational waves would offer a direct evidence of inflation and valuable insights into the dynamics of the early universe. During post-inflation reheating period, when the inflaton coherently oscillates at the bottom of its potential, primordial stochastic gravitational waves may be sourced by its perturbative decay into particles of different spins. Assuming the behavior of the potential near the minimum as a polynomial $V(φ)\sim φ^k$, where $k\ge 2$, and treating the inflaton as coherently oscillating classical field, we calculate the decay of inflaton into a pair of spin $3/2$ particles accompanied by graviton emission. We numerically study the reheating dynamics and calculate the stochastic gravitational wave spectra. Our analysis shows that the gravitational wave spectra can offer insights into the microscopic physics during inflation.

Figures (6)

• Figure 1: The Feynman diagrams for the three-body bremsstrahlung decay $\phi \to \psi_\mu{\psi_\mu} h_{\mu\nu}$. The $\psi_\mu$ is represented by $\psi$ and the graviton is represented by $h$.
• Figure 2: Evolution of inflaton energy density $\rho_\phi$ and radiation energy density $\rho_R$ as a function of the scale factor $a$ for $k = 2,4,6,8$. The coupling constant are set as follows: $\lambda_s=0$ and $\lambda_p=10^{-6}$ and $m_{3/2}=5\times 10^{-2}m_\phi$. A similar plot is obtained for non-zero $\lambda_s$ and $\lambda_p=0$.
• Figure 3: GW spectra coming from different harmonics for $k=6$.
• Figure 4: Sensitivity of the GW spectra for $k=6$ to the coupling constant $\lambda_p$ with $\lambda_s=0$.
• Figure 5: Sensitivity of the GW spectra for $k=6$ to masses of the RS field for a fixed $\lambda_p$ and $\lambda_s=0$.