2001/02/21 by Jaume Garriga, Alexander Vilenkin · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Cutoff #Earth Systems and Cosmic Evolution #Generalization #Inflation (cosmology) #Invariant (physics) #Mathematical analysis #Mathematics #Physics #Probability distribution #Quantum mechanics #Range (aeronautics) #Space Science and Extraterrestrial Life #Statistical physics #Statistics #Theoretical physics #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.64.023507
published as Phys.Rev.D64:023507,2001 · 15 pages, 5 figures
arxiv created 2001/02/21 · openalex publication_date 2001/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Some of the parameters we call ``constants of nature'' may in fact be variables related to the local values of some dynamical fields. During inflation, these variables are randomized by quantum fluctuations. In cases when the variable in question (call it \ensuremathχ) takes values in a continuous range, all thermalized regions in the universe are statistically equivalent, and a gauge invariant procedure for calculating the probability distribution for \ensuremathχ is known. This is the so-called ``spherical cutoff method.'' In order to find the probability distribution for \ensuremathχ it suffices to consider a large spherical patch in a single thermalized region. Here, we generalize this method to the case when the range of \ensuremathχ is discontinuous and there are several different types of thermalized region. We first formulate a set of requirements that any such generalization should satisfy, and then introduce a prescription that meets all the requirements. We finally apply this prescription to calculate the relative probability for different bubble universes in the open inflation scenario.