Massless scalar field in de Sitter spacetime: unitary quantum time evolution

TL;DR

This paper demonstrates that a massless scalar field in de Sitter spacetime can be quantized with a unitary time evolution, challenging previous assertions and clarifying its relation to known invariant states.

Contribution

It proves the existence of an O(4)-invariant Fock quantization with unitary evolution for massless fields in de Sitter space, contradicting earlier claims.

Findings

Established unitary quantum evolution for massless scalar fields in de Sitter.

Connected this quantization to O(4)-invariant Hadamard states.

Clarified the relation to the Bunch-Davies vacuum.

Abstract

We prove that, under the standard conformal scaling, a massless field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. This result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.