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

E. T. Akhmedov, I. A. Belkovich, D. V. Diakonov, K. A. Kazarnovskii

Published 2024-11-04, updated 2024-12-16Version 2

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.