wall fluctuation mode if the bubble wall tension is small. Therefore, although even the dominant quadrupole component is suppressed by the factor $(1-\Omega_0)^2$, one can construct some models in which the deviation of $\Omega_{0}$ from unity is large enough to produce measurable effects. We also consider a more general class of models, where the false vacuum decay may occur due to Hawking-Moss tunneling, as well as the models involving more than one scalar field. We discuss scalar perturbations in these models and point out that a large set of such models is already ruled out by observational data, unless there was a very long stage of slow-roll inflation after the tunneling. These results show that observational data allow us to test various assumptions concerning the structure of the string theory potentials and the duration of the last stage of inflation.'
author:
- 'Daisuke Yamauchi$^{1,2}$'
- Andrei Linde$^3$
- Atsushi Naruko$^1$
- Misao Sasaki$^1$
- Takahiro Tanaka$^1$
title: Open inflation in the landscape
---

Introduction {#sec:introduction}
============

The recent observational data show that the universe is almost exactly flat, $\Omega_{0} = 1$ with accuracy of about 1% [@Komatsu:2010fb]. This result is in an excellent agreement with the predictions of the simplest 