Anomaly-Induced Inflaton Decay and Gravitino-Overproduction Problem

Abstract

We point out that the inflaton spontaneously decays into any gauge bosons and gauginos via the super-Weyl, Kahler and sigma-model anomalies in supergravity, once the inflaton acquires a non-vanishing vacuum expectation value. In particular, in the dynamical supersymmetry breaking scenarios, the inflaton necessarily decays into the supersymmetry breaking sector, if the inflaton mass is larger than the dynamical scale. This generically causes the overproduction of the gravitinos, which severely constrains the inflation models.

Figures (1)

• Figure 1: 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 (red) line is excluded for each case. For $m_\phi \gtrsim \Lambda$, we used the anomaly-induced inflaton decay into the hidden gauge/gauginos to estimate the gravitino abundance (\ref{['eq:grav-abu']}), while the gravitino pair production (\ref{['eq:grav-abu-pair']}) was used for $m_\phi \lesssim \Lambda$. The typical values of $\left\langle \phi \right\rangle$ and $m_\phi$ for the single-field new Izawa:1996dv, multi-field new Asaka:1999jb, hybrid Copeland:1994vg and smooth hybrid Lazarides:1995vr, and chaotic Kawasaki:2000yn inflation models are also shown. Note that we adopt the chaotic inflation model without discrete symmetries, in which case $\left\langle K_\phi\right\rangle$ is expected to be around the Planck scale.