Geometric Origin of Stokes Phenomenon for de Sitter Radiation

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.