Unitarity at the Late time Boundary of de Sitter

TL;DR

This paper investigates the unitarity of boundary operators in de Sitter spacetime, revealing that both real and imaginary weights can correspond to unitary representations, unlike in Anti de Sitter space.

Contribution

It constructs late time boundary operators for massive scalar fields in de Sitter space and identifies conditions under which these operators are unitary, including imaginary weights.

Findings

Purely imaginary weights correspond to unitary operators in de Sitter.

All constructed boundary operators have positive definite norm.

The work extends understanding of unitarity beyond Anti de Sitter scenarios.

Abstract

The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin among its unitary irreducible representations. These unitary representations are labeled by the spin and the weight contribution to the scaling dimension and depending on the mass and spin of the field the weight may take either purely real or purely imaginary values. In this work, we construct the late time boundary operators for a massive scalar field propagating in de Sitter spacetime, in arbitrary dimensions. We show that contrary to the case of Anti de Sitter, purely imaginary weights also correspond to unitary operators, as well as the ones with real weight, and identify the corresponding unitary representations. We demonstrate that these operators correspond to the late time boundary operators and elucidate that all of them have positive definite norm.