Inflaton Decay in Supergravity

TL;DR

This work analyzes how inflaton decays in supergravity generate gravitinos through three main channels: direct pair production, spontaneous decay into the SUSY-breaking sector, and anomaly-induced decay into gauge sectors. The decay rates depend on the inflaton mass $m_\phi$, its VEV $\langle\phi\rangle$, the gravitino mass $m_{3/2}$, and the structure of the Kahler potential (minimal vs sequestered), with key expressions $\Gamma^{({\rm grav})} \sim \frac{|G_\phi|^2}{288\pi}\frac{m_\phi^5}{m_{3/2}^2 M_P^2}$ and $\Gamma^{({\rm anomaly})} \sim \frac{N_g \alpha^2}{256\pi^3}|X_G|^2 m_\phi^3$. The authors show that non-thermal gravitino production often imposes stringent constraints on inflation models and SUSY-breaking scenarios (particularly gravity mediation), complementing thermally produced gravitino limits that depend on the reheating temperature $T_R$. They discuss how the Kahler potential choice, hidden-sector dynamics, and possible symmetries of the inflaton can mitigate or exacerbate the problem, and they explore concrete inflation scenarios (single- and multi-field) to illustrate the resulting constraints. The findings imply that the cosmological gravitino problem provides a powerful, model-dependent yardstick for selecting viable high-scale inflation and SUSY-breaking frameworks, with potential resolutions including conformal dynamics, entropy production, or symmetry protections. Overall, the work connects early-un universe dynamics to high-energy model-building and offers guidance for future collider and cosmology-era tests.

Abstract

We discuss inflaton decay in supergravity, taking account of the gravitational effects. It is shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton generically decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. We derive constraints on both inflation models and supersymmetry breaking scenarios for avoiding overproduction of the gravitinos. Furthermore, the inflaton naturally decays into the visible sector via the top Yukawa coupling and SU(3)_C gauge interactions.

Figures (5)

• Figure 1: The decay of the inflaton into the three-body final states; the decay with the four-point vertex, and with the fermion and scalar exchanges, from left to right.
• Figure 2: Contours of the lower bound on $T_R$ in units of GeV. We set $g_* \;=\; 228.75$ and $Y_t \;=\; 0.6$. For details of the models, see Sec. \ref{['sec:models']}.
• Figure 3: Constraints from the gravitino production by the inflaton decay, for $m_{3/2} = 1{\rm\,TeV}$ with $B_h = 1$ (case A), $m_{3/2} = 1{\rm\,TeV}$ with $B_h = 10^{-3}$ (case B), $m_{3/2} = 100{\rm\,TeV}$ (case C), and $m_{3/2} = 1{\rm\,GeV}$ (case D). The region above the solid (gray) line is excluded for each case. For $m_\phi \gtrsim \Lambda$, we have used the anomaly-induced inflaton decay into the hidden gauge/gauginos to estimate the gravitino abundance, while the gravitino pair production has been used for $m_\phi \lesssim \Lambda$. Since $T_R$ is set to be the highest allowed value, the constraints shown in this figure are the most conservative ones.
• Figure 4: Constraints from the gravitino production by the inflaton decay, for $m_{3/2} = 1{\rm\,GeV}$ (left-upper), $m_{3/2} = 1{\rm\,TeV}$ with $B_h = 1$ and $10^{-3}$ (right-upper), $m_{3/2} = 100{\rm\,TeV}$ (bottom). We have set $\left\langle \phi \right\rangle = 10^{15}$GeV. The region surrounded by the solid line is allowed for each case.
• Figure 5: Constraints from the gravitino production by the inflaton decay, for $\left\langle \phi \right\rangle = 10^{12}, 10^{15}$ and $10^{18}$GeV. The region above the thick solid line is excluded. We also show the constraint for the unstable gravitino with $B_h = 10^{-3}$ as the thin (blue) line. For the region above the dashed (pink) line, we adopt (\ref{['Y32-anomaly']}), while (\ref{['Y32-pair']}) is used for the region below the dashed line. Since $T_R$ is set to be the highest allowed value, the constraints shown in this figure are the most conservative ones.