How many universes are in the multiverse?

Abstract

We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant Λthe number of distinguishable universes is bounded by e^{|Λ|^{-3/4}}. In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.

12 pages, minor changes

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Cited by in corpus (20)

• The Degree of Fine-Tuning in our Universe -- and Others
• The No-Boundary Measure in the Regime of Eternal Inflation
• Deformation of the Wheeler-DeWitt Equation
• Saturating the holographic entropy bound
• Can the Arrow of Time be understood from Quantum Cosmology?
• Minimal and maximal lengths from position-dependent noncommutativity
• Eternal Inflation, Global Time Cutoff Measures, and a Probability Paradox
• Deformation of Second and Third Quantization
• Fourth Quantization
• Conceptual Challenges on the Road to the Multiverse
• Agnesi Weighting for the Measure Problem of Cosmology
• Dynamical systems of eternal inflation: A possible solution to the problems of entropy, measure, observables and initial conditions
• Towards a non-anthropic solution to the cosmological constant problem
• Life, the Universe, and almost Everything: Signs of Cosmic Design?
• The Day the Universes Interacted: Quantum Cosmology without a Wave function
• Observational Imprints of Our Lost Twin Anti-Universe
• An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning
• Observability of the total inflationary expansion
• On the Cardinality of Future Worldlines in Discrete Spacetime Structures
• The Observer Class Hypothesis