The Stokes Phenomenon and Quantum Tunneling for de Sitter Radiation in Nonstationary Coordinates

TL;DR

This paper investigates quantum tunneling of de Sitter radiation in nonstationary coordinates, employing phase-integral methods to derive particle production rates and address the factor of two problem.

Contribution

It introduces a phase-integral approach in complex time to accurately compute tunneling rates in nonstationary de Sitter spacetimes, resolving existing methodological issues.

Findings

Derived particle-production rates in planar and global coordinates.

Identified sinusoidal factors depending on spacetime dimensionality.

Resolved the factor of two problem in tunneling calculations.

Abstract

We study quantum tunneling for the de Sitter radiation in the planar coordinates and global coordinates, which are nonstationary coordinates and describe the expanding geometry. Using the phase-integral approximation for the Hamilton-Jacobi action in the complex plane of time, we obtain the particle-production rate in both coordinates and derive the additional sinusoidal factor depending on the dimensionality of spacetime and the quantum number for spherical harmonics in the global coordinates. This approach resolves the factor of two problem in the tunneling method.