A prescription for probabilities in eternal inflation

Abstract

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 $\chi$) 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 $\chi$ is known. This is the so-called ``spherical cutoff method''. In order to find the probability distribution for $\chi$ 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 $\chi$ 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.

15 pages, 5 figures

Cited by in corpus (47)

• Dimensionless constants, cosmology and other dark matters
• Eternal inflation and its implications
• Inflationary paradigm in trouble after Planck2013
• Observational Consequences of a Landscape
• Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points
• What does inflation really predict?
• Probabilities in the inflationary multiverse
• Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem
• Holographic probabilities in eternal inflation
• TASI Lectures on the Cosmological Constant
• Inflationary Cosmology: Exploring the Universe from the Smallest to the Largest Scales
• Is Our Universe Likely to Decay within 20 Billion Years?
• A paradox in the global description of the multiverse
• Spontaneous Inflation and the Origin of the Arrow of Time
• Domain walls, near-BPS bubbles, and probabilities in the landscape
• Towards a gauge invariant volume-weighted probability measure for eternal inflation
• Hurdles for Recent Measures in Eternal Inflation
• Density Perturbations and the Cosmological Constant from Inflationary Landscapes
• Can Universe Experience Many Cycles with Different Vacua ?
• The Cold Big-Bang Cosmology as a Counter-example to Several Anthropic Arguments
• Counting Pockets with World Lines in Eternal Inflation
• Dark energy equation of state and anthropic selection
• Return of the Boltzmann Brains
• Multiple universes, cosmic coincidences, and other dark matters
• A measure of the multiverse
• Probabilities in the landscape: The decay of nearly flat space
• Landscape Predictions from Cosmological Vacuum Selection
• The Born Rule Dies
• Cycles in the Multiverse
• Cosmological Measures without Volume Weighting
• Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions
• Dynamics of the Inflationary Flow Equations
• Dynamics of M-theory vacua
• The Multiverse and Particle Physics
• Measures on transitions for cosmology from eternal inflation
• A perspective on the landscape problem
• Islands in the landscape
• The scale of gravity and the cosmological constant within a landscape
• Quantum cosmology and eternal inflation
• Anthropic prediction in a large toy landscape
• Time-reparametrization invariance in eternal inflation
• Taming the Runaway Problem of Inflationary Landscapes
• A Finite Measure for the Initial Conditions of Inflation
• Anthropic prediction for a large multi-jump landscape
• Agnesi Weighting for the Measure Problem of Cosmology
• Bayesian Reasoning in Eternal Inflation: A Solution to the Measure Problem
• Entanglement entropy of Primordial Black Holes after inflation