Open inflation in the landscape
  Open inflation scenario is attracting a renewed interest in the context of
string landscape. Since there are a large number of metastable de Sitter vacua
in string landscape, tunneling transitions to lower metastable vacua through
the bubble nucleation occur quite naturally. Although the deviation of Omega_0
from unity is small by the observational bound, we argue that the effect of
this small deviation on the large angle CMB anisotropies can be significant for
tensor-type perturbation in open inflation scenario. We consider the situation
in which there is a large hierarchy between the energy scale of the quantum
tunneling and that of the slow-roll inflation in the nucleated bubble. If the
potential just after tunneling is steep enough, a rapid-roll phase appears
before the slow-roll inflation. In this case the power spectrum is basically
determined by the Hubble rate during the slow-roll inflation. If such
rapid-roll phase is absent, the power spectrum keeps the memory of the high
energy density there in the large angular components. The amplitude of large
angular components can be enhanced due to the effects of the wall fluctuation
mode if the bubble wall tension is small. Therefore, 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.
