Ben Freivogel

Observational consequences of a landscape

In this paper we consider the implications of the ``landscape paradigm [1], [2] for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the ``overshoot problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.

Inflation in AdS/CFT.

We study the AdS/CFT correspondence as a probe of inflation. We assume the existence of a string landscape containing at least one stable AdS vacuum and a (nearby) metastable de Sitter state. Standard arguments imply that the bulk physics in the vicinity of the AdS minimum is described by a boundary CFT. We argue that large enough bubbles of the dS phase, including those able to inflate, are described by mixed states in the CFT. Inflating degrees of freedom are traced over and do not appear explicitly in the boundary description. They nevertheless leave a distinct imprint on the mixed state. Analytic continuation allows us, in principle, to recover a large amount of nonperturbatively defined information about the inflating regime. Our work also shows that no scattering process can create an inflating region, even by quantum tunneling, since a pure state can never evolve into a mixed state under unitary evolution.

Holographic framework for eternal inflation

In this paper we provide some circumstantial evidence for a holographic duality between bubble nucleation in an eternally inflating universe and a Euclidean conformal field theory (CFT). The holographic correspondence (which is different than Stromingers de Sitter (dS)/CFT duality) relates the decay of (3+1)-dimensional de Sitter space to a two-dimensional CFT. It is not associated with pure de Sitter space, but rather with Coleman-De Luccia bubble nucleation. Alternatively, it can be thought of as a holographic description of the open, infinite, Friedmann-Robertson-Walker (FRW) cosmology that results from such a bubble. The conjectured holographic representation is of a new type that combines holography with the Wheeler-DeWitt formalism to produce a Wheeler-DeWitt theory that lives on the spatial boundary of a k=-1 FRW cosmology. We also argue for a more ambitious interpretation of the Wheeler-DeWitt CFT as a holographic dual of the entire Landscape.

Framework for the string theory landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background, and that it contains metastable de Sitter space as an intermediate state.

Boltzmann babies in the proper time measure

After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well defined, and consistent with observation. This allows us to proceed by elimination. As an example, we consider the proper time cutoff on a geodesic congruence. It predicts that typical observers are quantum fluctuations in the early universe, or Boltzmann babies. We sharpen this well-known youngness problem by taking into account the expansion and open spatial geometry of pocket universes. Moreover, we relate the youngness problem directly to the probability distribution for observables, such as the temperature of the cosmic background radiation. We consider a number of modifications of the proper time measure, but find none that would make it compatible with observation.

Colliding with a crunching bubble

In the context of eternal inflation we discuss the fate of Lambda = 0 bubbles when they collide with Lambda< 0 crunching bubbles. When the Lambda = 0 bubble is supersymmetric, it is not completely destroyed by collisions. If the domain wall separating the bubbles has higher tension than the BPS bound, it is expelled from the Lambda = 0 bubble and does not alter its long time behavior. If the domain wall saturates the BPS bound, then it stays inside the Lambda = 0 bubble and removes a finite fraction of future infinity. In this case, the crunch singularity is hidden behind the horizon of a stable hyperbolic black hole.

Probabilities in the landscape: The Decay of nearly flat space

We discuss aspects of the problem of assigning probabilities in eternal inflation. In particular, we investigate a recent suggestion that the lowest energy de Sitter vacuum in the landscape is effectively stable. The associated proposal for probabilities would relegate lower energy vacua to unlikely excursions of a high entropy system. We note that it would also imply that the string theory landscape is experimentally ruled out. However, we extensively analyze the structure of the space of Coleman-De Luccia solutions, and we present analytic arguments, as well as numerical evidence, that the decay rate varies continuously as the false vacuum energy goes through zero. Hence, low-energy de Sitter vacua do not become anomalously stable; negative and zero-cosmological constant regions cannot be neglected.

Future foam: Nontrivial topology from bubble collisions in eternal inflation

We study pocket universes which have zero cosmological constant and nontrivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin-wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.

Asymptotic states of the bounce geometry

We consider the question of asymptotic observables in cosmology. We assume that string theory contains a landscape of vacua, and that metastable de Sitter regions can decay to a zero cosmological constant by bubble nucleation. The asymptotic properties of the corresponding bounce solution should be incorporated in a nonperturbative quantum theory of cosmology. A recent proposal for such a framework defines an S matrix between the past and future boundaries of the bounce. We analyze in detail the properties of asymptotic states in this proposal, finding that generic small perturbations of the initial state cause a global crunch. We conclude that late-time amplitudes should be computed directly. This would require a string theory analog of the no-boundary proposal.