De Sitter space as BRST invariant coherent state of gravitons

TL;DR

This paper constructs a BRST-invariant coherent state of gravitons to represent de Sitter space within quantum gravity, ensuring gauge consistency and capturing phenomena like Gibbons-Hawking radiation.

Contribution

It introduces a novel BRST-invariant coherent state framework for de Sitter space, extending previous ideas with a focus on gauge invariance and collective quantum effects.

Findings

De Sitter space can be represented as a BRST-invariant graviton coherent state.

In the species limit, quantum gravitational effects vanish, making the construction exact.

The approach allows calculation of phenomena like Gibbons-Hawking radiation.

Abstract

The $S$-matrix formulation indicates that a consistent embedding of de Sitter state in quantum gravity is possible exclusively as an excited quantum state constructed on top of a valid $S$-matrix vacuum such as Minkowski. In the present paper we offer such a construction of de Sitter in the form of a coherent state of gravitons. Unlike previous realizations of this idea, we focus on BRST invariance as the guiding principle for physicality. In order to establish the universal rules of gauge consistency, we study the BRST-invariant construction of coherent states created by classical and quantum sources in QED and in linearized gravity. Introduction of $N$ copies of scalar matter coupled to gravity allows us to take a special double scaling limit, a so-called species limit, in which our construction of de Sitter becomes exact. In this limit, the irrelevant quantum gravitational effects vanish whereas the collective phenomena, such as Gibbons-Hawking radiation, are calculable.