Quantum Dynamics for de Sitter Radiation

TL;DR

This paper analyzes quantum particle production in de Sitter space using Hamiltonian formalism, comparing in-out and Gibbons-Hawking approaches, revealing discrepancies in radiation predictions.

Contribution

It introduces a Hamiltonian approach with invariant operators for scalar fields in de Sitter space and compares particle production results from different formalisms.

Findings

In-out formalism yields different particle production rates than Gibbons-Hawking method.

Exact Gaussian wave functions are constructed for each Fourier mode.

Discrepancies between formalisms are discussed and analyzed.

Abstract

We revisit the Hamiltonian formalism for a massive scalar field and study the particle production in a de Sitter space. In the invariant-operator picture the time-dependent annihilation and creation operators are constructed in terms of a complex solution to the classical equation of motion for the field and the Gaussian wave function for each Fourier mode is found which is an exact solution to the Schr\"odinger equation. The in-out formalism is reformulated by the annihilation and creation operators and the Gaussian wave functions. The de Sitter radiation from the in-out formalism differs from the Gibbons-Hawking radiation in the planar coordinates, and we discuss the discrepancy of the particle production by the two method