Inflaton Decay through Supergravity Effects

TL;DR

This paper demonstrates that supergravity effects grant the inflaton the ability to decay into all matter fields once the inflaton acquires a nonzero vacuum expectation value, immediately producing gravitinos and imposing a lower bound on the reheating temperature. The authors derive explicit decay rates for three-body inflaton decays and show how these channels yield a lower $T_R$ via the top Yukawa coupling, while also enabling gravitino production from decays into the SUSY-breaking sector. They quantify the resulting constraints on inflaton mass and VEV, revealing that high-scale inflation models such as hybrid and smooth hybrid inflation face strong gravitino- and reheating-temperature limits, whereas chaotic inflation can be made viable with appropriate symmetries that suppress problematic linear terms in the Kähler potential. The results underscore a generic tension between large-field inflation and SUSY-breaking phenomenology, with implications for model-building, leptogenesis, and hidden-sector construction.

Abstract

We point out that supergravity effects enable the inflaton to decay into all matter fields, including the visible and the supersymmetry breaking sectors, once the inflaton acquires a non-vanishing vacuum expectation value. The new decay processes have great impacts on cosmology; the reheating temperature is bounded below; the gravitinos are produced by the inflaton decay in a broad class of the dynamical supersymmetry breaking models. We derive the bounds on the inflaton mass and the vacuum expectation value, which severely constrain high-scale inflations such as the hybrid and chaotic inflation models.

Figures (4)

• Figure 1: Contours of the lower bound on the reheating temperature $T_R$, denoted by the solid lines. We set $g_* \;=\; 228.75$ and $Y_t \;=\; 0.6$. The typical values of $\left\langle \phi \right\rangle$ and $m_\phi$ for the hybrid and smooth hybrid inflation models ($n= 2, \,3$ and $4$ from left to right) are also shown.
• Figure 2: Constraints from the abundance of the gravitino produced from the inflaton decay, for $m_{3/2} = 1{\rm\,GeV}$. We set $g_* \;=\; 228.75$ and $C \;=\; 1$. The region above the solid line is excluded. $T_R$ is set to be the largest allowed value, and the bound becomes severer for lower $T_R$. The vertical dotted line corresponds to $m_\phi = \sqrt{m_{3/2} M_P}$. For $m_\phi \mathop{}_{ \sim}^{ <} \sqrt{m_{3/2} M_P}$, the inflaton decay into the SUSY breaking sector is expected to be kinematically forbidden; however the gravitino pair production instead puts a severer constraint moduliAsaka:2006bvDine:2006iiEndo:2006tf. The typical values of $\left\langle \phi \right\rangle$ and $m_\phi$ for the hybrid and smooth hybrid inflation models are also shown.
• Figure 3: Same as Fig. \ref{['fig:1GeV']} but for $m_{3/2} = 1{\rm\,TeV}$. The solid and dashed lines are for the hadronic branching ratio $B_h = 1$ and $10^{-3}$, respectively.
• Figure 4: Same as Fig. \ref{['fig:1GeV']} but for $m_{3/2} = 100{\rm\,TeV}$.