We discuss the possibility to construct supergravity models with a single superfield describing inflation as well as the tiny cosmological constant $V sim 10^{{-120}}$. One could expect that the simplest way to do it is to study models with a supersy
mmetric Minkowski vacuum and then slightly uplift them. However, due to the recently proven no-go theorem, such a tiny uplifting cannot be achieved by a small modification of the parameters of the theory. We illustrate this general result by investigation of models with a single chiral superfield recently proposed by Ketov and Terada. We show that the addition of a small constant or a linear term to the superpotential of a model with a stable supersymmetric Minkowski vacuum converts it to an AdS vacuum, which results in a rapid cosmological collapse. One can avoid this problem and uplift a supersymmetric Minkowski vacuum to a dS vacuum with $V_{0}sim 10^{-120}$ without violating the no-go theorem by making these extra terms large enough. However, we show that this leads to a strong supersymmetry breaking in the uplifted vacua.
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 nucleati
on 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.
To make predictions for an eternally inflating multiverse, one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes coolin
g from hot big bang conditions - must not be vastly outnumbered by Boltzmann brains - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.
