New ground state for quantum gravity

TL;DR

This paper proposes a new quantum gravity ground state that serves as a vacuum for gravitons, contrasting it with the Kodama state and emphasizing the importance of a non-perturbative approach.

Contribution

It introduces a novel explicit perturbative ground state in quantum gravity, dependent on the Immirzi parameter, and clarifies why the Kodama state is unphysical for gravitons in de Sitter space.

Findings

The new state is chiral and dependent on the Immirzi parameter.

The Kodama state describes unphysical self-dual excitations.

The proposed state is the vacuum of a second quantized graviton theory.

Abstract

In this paper we conjecture the existence of a new "ground" state in quantum gravity, supplying a wave function for the inflationary Universe. We present its explicit perturbative expression in the connection representation, exhibiting the associated inner product. The state is chiral, dependent on the Immirzi parameter, and is the vacuum of a second quantized theory of graviton particles. We identify the physical and unphysical Hilbert sub-spaces. We then contrast this state with the perturbed Kodama state and explain why the latter can never describe gravitons in a de Sitter background. Instead, it describes self-dual excitations, which are composites of the positive frequencies of the right-handed graviton and the negative frequencies of the left-handed graviton. These excitations are shown to be unphysical under the inner product we have identified. Our rejection of the Kodama state has a moral tale to it: the semi-classical limit of quantum gravity can be the wrong path for making contact with reality (which may sometimes be perturbative but nonetheless fully quantum). Our results point towards a non-perturbative extension, and we present some conjectures on the nature of this hypothetical state.