down [@Linde:1998iw; @Linde:1999wv].

This intermediate regime may last for a long time if the field potential is steep after tunneling. In general, this may be a typical situation during the tunneling in the string landscape scenario. As we mentioned in the introduction, the tunneling in the landscape may occur from a metastable vacuum with a very high value of energy density. Unless we have some specific knowledge about this vacuum state, one may assume that the scale of the energy density of this vacuum may be $O(1)$ in Planck units, or it may take some value on the grand unification energy scale $\sim 10^{-10}$. Meanwhile in many models of the slow-roll inflation based on string theory with vacuum stabilization, the Hubble constant must be smaller than the gravitino mass [@Kallosh:2004yh]. Although it is possible to avoid this conclusion, it is very hard to do it without fine-tuning. If the gravitino mass is of the order $1$ TeV or lower, the corresponding vacuum energy density during the last stage of the slow-roll inflation should be smaller than $10^{-30}$, in Planck units.

Our knowledge of the string landscape is very incomplete, so one should not fully rely on the estimates given above. 