Geometric Origin of Stokes Phenomenon for de Sitter Radiation

TL;DR

This paper offers a geometric interpretation of the Stokes phenomenon in de Sitter spacetime, explaining particle production differences between even and odd dimensions through complex-time path analysis.

Contribution

It introduces a novel geometric framework linking Stokes phenomenon to particle production in de Sitter space using complex-time paths.

Findings

Particles produced in even dimensions, not in odd dimensions

Scattering amplitude explains Boltzmann factor and sinusoidal behavior

Interference among four closed paths causes Stokes phenomenon

Abstract

We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the transported one along a closed path in the complex-time plane gives the particle-production rate that explains not only the Boltzmann factor from the simple pole at infinity, corresponding to the cosmological horizon, but also the sinusoidal behavior from simple poles at the north and south poles of the Euclidean geometry. The Stokes phenomenon is a consequence of interference among four independent closed paths in the complex plane.