A Measure of the multiverse

  title={A Measure of the multiverse},
  author={Alexander Vilenkin},
  journal={Journal of Physics A},
  • A. Vilenkin
  • Published 2006
  • Computer Science, Economics, Physics
  • Journal of Physics A
I review recent progress in defining a probability measure in the inflationary multiverse. General requirements for a satisfactory measure are formulated and recent proposals for the measure are clarified and discussed. 
Eternal Inflation and the Measure Problem
The present course does, of course, assume General Relativity as a prerequisite. Since most relativity courses include some cosmology, it appears logical to assume that the reader will also beExpand
Freak observers and the measure of the multiverse
I suggest that the factor pj in the pocket-based measure of the multiverse, Pj = pj fj, should be interpreted as accounting for equilibrium de Sitter vacuum fluctuations, while the selection factorExpand
Measures for a Transdimensional Multiverse
The multiverse/landscape paradigm that has emerged from eternal inflation and string theory, describes a large-scale multiverse populated by "pocket universes" which come in a huge variety ofExpand
Volume-weighted measure for eternal inflation
I propose a new volume-weighted probability measure for cosmological 'multiverse' scenarios involving eternal inflation. The 'reheating-volume (RV) cutoff' calculates the distribution of observableExpand
String cosmology: a review
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspectsExpand
Reheating-volume measure for random-walk inflation
The recently proposed ``reheating-volume'' (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological multiverse scenarios involving eternalExpand
Measure and Probability in Cosmology
General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. In ordinary statistical physics, the Liouville measure is used toExpand
A stochastic measure for eternal inflation
We use the stochastic approach to investigate a measure for slow roll eternal inflation. The probability for the universe to have a given Hubble radius can be calculated in this framework. In aExpand
Toward inflation models compatible with the no-boundary proposal
In this paper, we investigate various inflation models in the context of the no-boundary proposal. We propose that a good inflation model should satisfy three conditions: observational constraints,Expand
The distribution of Omega_k from the scale-factor cutoff measure
Our universe may be contained in one among a diverging number of bubbles that nucleate within an eternally inflating multiverse. A promising measure to regulate the diverging spacetime volume of suchExpand


The fractal dimension of the inflationary universe
Abstract In cosmological scenarios of the new inflationary type, inflation never ends completely. The total volume of inflating regions grows exponentially with time, and they form a self-similarExpand
Prescription for probabilities in eternal inflation
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 quantumExpand
Inflation and eternal inflation
Abstract The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternalExpand
The Anthropic Landscape of String Theory
In this lecture I make some educated guesses, about the landscape of string theory vacua. Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably largeExpand
Predictability crisis in inflationary cosmology and its resolution
Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today'sExpand
Observational consequences of a landscape
In this paper we consider the implications of the ``landscape paradigm [1], [2] for the large scale properties of the universe. The most direct implication of a rich landscape is that our localExpand
Regularization scheme dependence of predictions in inflationary cosmology.
  • Linde, Mezhlumian
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1996
It is argued that at the current level of understanding, the simple regularization schemes associated with cutoffs at equal time hypersurfaces are as good as the recently proposed more complicated procedures which try to fix the time-reparametrization dependence. Expand
Holographic probabilities in eternal inflation.
  • R. Bousso
  • Physics, Medicine
  • Physical review letters
  • 2006
It is proposed to estimate the probability for observers to emerge in a given vacuum by the entropy that can be produced in a local patch, which allows for prior-free predictions. Expand
Eternally existing self-reproducing chaotic inflanationary universe
It is shown that the large-scale quantum fluctuations of the scalar field ϕ generated in the chaotic-inflation scenario lead to an infinite process of self-reproduction of inflationary mini-universe.Expand
Probabilities in the Bousso–Polchinski multiverse
Using the recently introduced method to calculate bubble abundances in an eternally inflating spacetime, we investigate the volume distribution for the cosmological constant Λ in the context of theExpand