Probability of Slowroll Inflation in the Multiverse

Slowroll after tunneling is a crucial step in one popular framework of the multiverse---false vacuum eternal inflation (FVEI). In a landscape with a large number of fields, we provide a heuristic estimation for its probability. We find that the chance to slowroll is exponentially suppressed, where the exponent comes from the number of fields. However, the relative probability to have more e-foldings is only mildly suppressed as $N_e^{-\alpha} $ with $\alpha\sim3$. Base on these two properties, we show that the FVEI picture is still self-consistent and may have a strong preference between different slowroll models.