Probabilities in the inflationary multiverse

TL;DR

Probabilities in the inflationary multiverse develops a two-component framework for predicting observed constants across a landscape of vacua. It combines internal pocket distributions $P(X;j)$, derived from diffusion-ergodic thinking and slow-roll expansion, with pocket-type abundances $p_j$ obtained via comoving-horizon cutoff counting, to form the full distribution $P_{obs}(X) \propto \sum_j p_j P(X;j)\, n_{obs}^{(j)}(X)$. The internal distributions are anchored by the ergodic conjecture, e.g., $P_q(X) \propto H^{-2}(X)\exp[S(X)]$ on the slow-roll boundary, while pocket abundances are computed through either bubble-nucleation (CHC) or diffusion (FP) frameworks; the comoving probability $p_j^c$ is shown to have limitations. The resulting full distribution provides a tractable path to predictions in string theory landscapes, with explicit formulas linking pocket physics, expansion, and observer counts. The work clarifies when different weighting schemes agree or diverge and offers a concrete route to connecting high-energy theory with cosmological observables across a 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.

Figures (2)

• Figure 1: Structure of eternally inflating spacetime. Thermalized regions are shown by dark shading.
• Figure 2: Structure of a pocket universe.