The Polonyi Problem and Upper bound on Inflation Scale in Supergravity

TL;DR

The study tackles the Polonyi problem in gravity-mediation SUSY breaking, showing that a linear term in the Kahler potential can revive the problem even with dynamical SUSY breaking by destabilizing the Polonyi field during inflation. It derives an upper bound on the new scale $M_{*}$, finding $M_{*} \lesssim 10^{12-13}$ GeV, which ties $M_{*}$ to the dynamical SUSY-breaking scale $\Lambda_{\rm SUSY} \sim 10^{11}$ GeV. It then shows that the inflation scale must satisfy $H_{\rm inf} \lesssim 10^{8}$ GeV (unless $T_R$ is tiny), disfavouring many high-scale inflations and favoring certain low-scale models like a specific new-inflation scenario with $n=4$ that aligns with WMAP constraints. The authors conclude that the Polonyi problem may be absent in gauge- or anomaly-mediated SUSY breaking, but in gravity mediation it requires either a suppressed linear term or low-scale inflation for consistency. $

Abstract

We reconsider the Polonyi problem in gravity-mediation models for supersymmetry (SUSY) breaking. It has been argued that there is no problem in the dynamical SUSY breaking scenarios, since the Polonyi field acquires a sufficiently large mass of the order of the dynamical SUSY-breaking scale Lamada_{SUSY}. However, we find that a linear term of the Polonyi field in the Kahler potential brings us back to the Polonyi problem, unless the inflation scale is sufficiently low, H_{inf} < 10^{8} GeV, or the reheating temperature is extremely low, T_{R} < 100 GeV. Here, this Polonyi problem is more serious than the original one, since the Polonyi field mainly decays into a pair of gravitinos.

Figures (1)

• Figure 1: Schematic plots of the Polonyi potential during the inflation. Here, we assume that $\lambda = 4\pi$, $\xi = \eta' =1$, $c\simeq M_{G}$ and $m_{3/2}=1$ TeV. The potentials correspond to $H_{\rm inf} = 0$, $5\times 10^{6}\,{\rm GeV}$, $10^{8}\,{\rm GeV}$ from left to right, respectively.