On (dis)agreement between different methods of calculation of the imaginary part of the effective action in expanding space-times

TL;DR

This paper compares two methods for calculating the imaginary part of the effective action in expanding space-times, revealing discrepancies in eternal expansion scenarios due to initial and final state wave-functionals.

Contribution

It demonstrates the origin of differences between Bogolyubov and functional integral approaches in calculating effective action imaginary parts in expanding universes.

Findings

Different results from the two methods in eternal expansion cases

Discrepancies linked to initial and final state wave-functionals

Explicit example provided in de Sitter space-time

Abstract

We consider two approaches to calculate imaginary parts of effective actions in expanding space-times. While the first approach uses Bogolyubov coefficients, the second one uses the functional integral or the Feynman propagator. In eternally expanding space-times these two approaches give different answers for the imaginary parts. The origin of the difference can be traced to the presence if the wave-functionals for the initial and final states in the functional integral. We show this explicitly on the example of the expanding Poincare patch of the de Sitter space-time.