IR-fixed Euclidean vacuum for linearized gravity on de Sitter space

TL;DR

This paper investigates the Euclidean vacuum state for linearized gravity on de Sitter space, revealing gauge invariance and Hadamard properties, but also addressing issues of positivity through a low-energy modification.

Contribution

It introduces a method using Calderón projectors to construct a quantum state for linearized gravity on de Sitter space and proposes a modification to ensure positivity.

Findings

The Euclidean vacuum state is gauge invariant and Hadamard.

The state is not positive on the entire phase space.

A low-energy modification yields a positive, Hadamard state.

Abstract

We consider the Euclidean vacuum for linearized gravity on the global de Sitter space, obtained from the Euclidean Green's function on the 4-sphere. We use the notion of Calder\'on projectors to recover a quantum state for the Lorentzian theory on de Sitter space. We show that while the state is gauge invariant and Hadamard, it is not positive on the whole of the phase space. We show however that a suitable modification at low energies yields a well-defined Hadamard state on global de Sitter space.