Probabilities in the inflationary multiverse

Abstract

Inflationary cosmology leads to the picture of a "multiverse," involving an infinite number of (spatially infinite) post-inflationary thermalized regions, called pocket universes. In the context of theories with many vacua, such as the landscape of string theory, the effective constants of Nature are randomized by quantum processes during inflation. We discuss an analytic estimate for the volume distribution of the constants within each pocket universe. This is based on the conjecture that the field distribution is approximately ergodic in the diffusion regime, when the dynamics of the fields is dominated by quantum fluctuations (rather than by the classical drift). We then propose a method for determining the relative abundances of different types of pocket universes. Both ingredients are combined into an expression for the distribution of the constants in pocket universes of all types.

Inflation and String Theory

“…We have largely avoided discussing deep issues involving the initial conditions for inflation, including the global view of eternal inflation [822][823][824][825], the associated measure problem [826][827][828][829][830][831][832][833], and the geodesic incompleteness of inflation in the past [834]. String theory has inspired several compelling approaches to these questions, but no complete solutions have been advanced.…”

Dark Energy

“…However, it is rather difficult to realize this idea. A number of measures have been proposed in the literature, including the volume based measure [74] (see [75] with scale-factor cutoff), the local measure [76,77], the Liouville measure [78,79,80], the stochastic measure [81], and so on. However, there is so far no principle to determine which measure to use.…”

Predicting the cosmological constant with the scale-factor cutoff measure

“…One can define spacelike hypersurfaces separating the quantum and classical regimes (see for example Ref. [15]), which we denote by Σ q . In universes like ours, slow-roll inflation is followed by thermalization (reheating) and the standard post-inflationary evolution.…”