Gravitational Production of Spin-3/2 Particles During Reheating

TL;DR

This work shows that gravitational interactions at reheating inevitably produce spin-$\frac{3}{2}$ particles (raritrons) via inflaton condensate oscillations, with production dominated by the longitudinal mode and mediated by graviton exchange. The authors develop a general formalism for gravitino–like states, compute production rates for inflaton-condensate and thermal-bath sources across generic potentials, and extract the resulting relic abundance. They find a robust lower bound on the raritron/gravitino mass once cosmological constraints (notably BBN) are imposed, and demonstrate that gravitational production can far exceed thermal production in many regimes. The analysis is then specialized to gravitino dark matter, including toy models and a no-scale supergravity scenario, highlighting how goldstino/inflatino mixing and reheating dynamics shape nonthermal gravitino production, while standard thermal production remains subdominant in the explored parameter space. Overall, gravity-driven production during reheating imposes strong cosmological constraints on reheating temperatures and SUSY-breaking sectors, with significant implications for dark matter and early-Universe cosmology.

Abstract

We compute the density of a spin-$\frac32$ particle, the raritron, produced at the end of inflation due to gravitational interactions. We consider a background inflaton condensate as the source of this production, mediated by the exchange of a graviton. This production greatly exceeds the gravitational production from the emergent thermal bath during reheating. The relic abundance limit sets an absolute minimum mass for a stable raritron, though there are also model dependent constraints imposed by unitarity. We also examine the case of gravitational production of a gravitino, taking into account the goldstino evolution during reheating. We compare these results with conventional gravitino production mechanisms.

Figures (7)

• Figure 1: Feynman diagram for the production of spin-$\frac{3}{2}$ particles through the gravitational scattering of the inflaton condensate or the Standard Model particle bath.
• Figure 2: Longitudinal and transverse raritron production rates for $k=2$ in the units of $R \times M_P^4/\rho_{\phi}^2$ as a function of $\tau = m_{3/2}^2/m_{\phi}^2$. As can be seen from the figure, the raritron production is completely dominated by the longitudinal component, which contains a factor $\tau^{-1}$.
• Figure 3: Contours of $\Omega_{\rm cond} h^2 = 0.12$ (red) and $\Omega_{\rm thermal} h^2 = 0.12$ (blue) in the $(m_{3/2}, T_{\rm RH})$ plane.
• Figure 4: Feynman diagrams of the dark matter production processes.
• Figure 5: The $(m_{\psi},T_{\rm RH})$ plane showing lines for $\Omega_\psi h^2=0.12$ with $m_\chi/m_\phi = 1$ and 10 as labeled as well as $y=1$, $m_\phi=1.7\times10^{13}$ GeV, and $\rho_{\rm end}=(5.2\times10^{15}~{\rm GeV})^4$. The red lines correspond to the relic density obtained from Eq. (\ref{['Opsi']}) which was derived from the Lagrangian in Eq. (\ref{['toy']}) (without the assumption $\tau_\chi \gg 1$). The blue lines show the analogous result derived from the Lagrangian (\ref{['toy2']}).