Eternal inflation and localization on the landscape
Abstract
Description
We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(ϕ)=V_{0}+δV(ϕ)$, where $|δV(ϕ)|\ll V_{0}$ is random. We find that the diffusion of the distribution function $ρ(ϕ,t)$ of the inflaton expectation value in different Hubble patches may be suppressed due to the effect analogous to the Anderson localization in disordered quantum systems. At $t \to \infty$ only the localized part of the distribution function $ρ(ϕ, t)$ survives which leads to dynamical selection principle on the landscape. The probability to measure any but a small value of the cosmological constant in a given Hubble patch on the landscape is exponentially suppressed at $t\to \infty$.
4 pages; more references added; discussion enlarged
4 pages; more references added; discussion enlarged