A Stochastic Measure for Eternal Inflation

Abstract

We use the stochastic approach to investigate the measure for slow roll eternal inflation. The probability for the universe of a given Hubble radius can be calculated in this framework. In a solvable model, it is shown that the probability for the universe to evolve from a state with a smaller Hubble radius to that of a larger Hubble radius is dominated by the classical probability without the stochastic source. While the probability for the universe to evolve from a larger Hubble radius to a smaller one is suppressed by $\exp (-\Delta S)$, where the de Sitter entropy $S$ arises naturally in this stochastic approach.

11 pages, 1 figure

References in corpus (9)

• The Measure Problem in Cosmology
• Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem
• Holographic probabilities in eternal inflation
• Eternal Inflation: The Inside Story
• Towards a gauge invariant volume-weighted probability measure for eternal inflation
• Probabilities in the Bousso-Polchinski multiverse
• Eternal observers and bubble abundances in the landscape
• Probabilities in the landscape
• Is Noncommutative Eternal Inflation Possible?

Cited by in corpus (23)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Dark Energy
• Enhanced Non-Gaussianity from Excited Initial States
• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• General Single Field Inflation with Large Positive Non-Gaussianity
• Backreaction and Stochastic Effects in Single Field Inflation
• The Born Rule Dies
• Preventing eternality in phantom inflation
• Cosmological Measures without Volume Weighting
• New Agegraphic Dark Energy in Brans-Dicke Theory
• Testing models of inflation with CMB non-gaussianity
• Hawking-Moss transition with a black hole seed
• Agnesi Weighting for the Measure Problem of Cosmology
• On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
• Reconstructing quintom from WMAP 5-year observations: Generalized ghost condensate
• Is Non-minimal Inflation Eternal?
• Typicality, Freak Observers and the Anthropic Principle of Existence
• Life, the Universe, and almost Everything: Signs of Cosmic Design?
• Stochastic Inflation and Replica Field Theory
• Possible Anthropic Support for a Decaying Universe: A Cosmic Doomsday Argument
• Stochastic Eternal Inflation in a Bianchi Type I Universe
• Do Our Observations Depend upon the Quantum State of the Universe?