Unique fermionic vacuum in de Sitter spacetime from hybrid quantum cosmology

TL;DR

This paper demonstrates how a criterion from hybrid quantum cosmology uniquely determines the vacuum state for the Dirac field in de Sitter spacetime by analyzing asymptotic behavior of fermionic variables.

Contribution

It introduces a dynamical criterion based on asymptotic Hamiltonian diagonalization to select a unique fermionic vacuum in de Sitter space within quantum field theory in curved spacetime.

Findings

Unique fermionic vacuum in de Sitter spacetime identified.

Explicit basis of solutions for the Dirac equation constructed.

Fock representation uniquely determined by asymptotic expansion.

Abstract

In this work we show how the criterion of asymptotic Hamiltonian diagonalization originated in hybrid quantum cosmology serves to pick out a unique vacuum for the Dirac field in de Sitter, in the context of quantum field theory in curved spacetimes. This criterion is based on the dynamical definition of annihilation and creationlike variables for the fermionic field, which obey the linearized dynamics of a Hamiltonian that has been diagonalized in a way that is adapted to its local spatial structure. This leads to fermionic variables that possess a precise asymptotic expansion in the ultraviolet limit of large wavenumbers. We explicitly show that, when the cosmological background is fixed as a de Sitter solution, this expansion uniquely selects the choice of fermionic annihilation and creationlike variables for all spatial scales, and thus picks out a unique privileged Fock representation and vacuum state for the Dirac field in de Sitter. The explicit form of the basis of solutions to the Dirac equation associated with this vacuum is then computed.