The linearization of the Kodama state

TL;DR

This paper investigates the normalizability of the linearized Kodama state around deSitter spacetime, finding it non-normalizable in Lorentzian signature but delta-function normalizable in Euclidean signature, raising questions about its physical viability.

Contribution

It provides a detailed analysis of the normalizability of the linearized Kodama state in different spacetime signatures, challenging previous assumptions about its physical relevance.

Findings

Non-normalizable in Lorentzian theory

Delta-functional normalizable in Euclidean theory

Implications for the physical validity of the Kodama state

Abstract

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.