Probability of Slowroll Inflation in the Multiverse

TL;DR

This paper estimates the probability of slowroll inflation after tunneling in the multiverse, finding it exponentially suppressed with a mild suppression for more e-foldings, supporting the consistency of false vacuum eternal inflation.

Contribution

It provides a heuristic estimation of slowroll probability in a multi-field landscape, highlighting the exponential suppression and mild dependence on e-foldings, which supports the viability of FVEI.

Findings

Slowroll probability is exponentially suppressed with the number of fields.

The probability of having more e-foldings is only mildly suppressed.

FVEI remains a self-consistent framework despite suppression factors.

Abstract

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.