Unitary Evolution and Cosmological Fine-Tuning

Abstract

Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein's equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories, less than $10^{-6.6\times 10^7}$. We argue that while inflation does not affect the number of initial conditions that evolve into a late universe like our own, it nevertheless provides an appealing target for true theories of initial conditions, by allowing for small patches of space with sub-Planckian curvature to grow into reasonable universes.

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Cited by in corpus (16)

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• Vacuum Structure and the Arrow of Time
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• Measure, Topology and Probabilistic Reasoning in Cosmology
• Robustness of inflation to kinetic inhomogeneities
• Clearing the Brush: The Last Stand of Solo Small Field Inflation
• Dynamical systems of eternal inflation: A possible solution to the problems of entropy, measure, observables and initial conditions
• The Continuum of Discrete Trajectories in Eternal Inflation
• Comments on the Canonical Measure in Cosmology
• The Fine-Tuning Argument
• Localization on the Landscape and Eternal Inflation
• Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis
• On the Carroll-Chen Model
• Holography as Cutoff: a proposal for measure of inflationary universes