Functional Approach to Stochastic Inflation
Yuri V. Shtanov (Bogolyubov Institute, Kiev, Ukraine, Brown, University, Providence, RI)
TL;DR
This paper introduces a functional approach to stochastic inflation, utilizing path integrals and saddle-point approximation to analyze scalar field probability distributions and inflationary history statistics.
Contribution
It presents a novel functional method for stochastic inflation dynamics based on path integral representation and saddle-point approximation, advancing analytical tools in the field.
Findings
Derived scalar field probability distributions of various types.
Developed statistics for inflationary-history-dependent functionals.
Provided analytical expressions for inflationary dynamics.
Abstract
We propose functional approach to the stochastic inflationary universe dynamics. It is based on path integral representation of the solution to the differential equation for the scalar field probability distribution. In the saddle-point approximation scalar field probability distributions of various type are derived and the statistics of the inflationary-history-dependent functionals is developed.
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