Path Integral for Stochastic Inflation: Non-Perturbative Volume Weighting, Complex Histories, Initial Conditions and the End of Inflation

Abstract

In this paper we present a path integral formulation of stochastic inflation, in which volume weighting can easily be implemented. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow-roll. The slow-roll end of inflation mitigates certain "Youngness Paradox"-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper time volume weighting as a viable measure for answering at least some interesting cosmological questions.

8 pages, 4 figures

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Cited by in corpus (4)

• 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
• Path Integral Approach to Uncertainties in SIR-type Systems
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond