The linearization of the Kodama state

Laurent Freidel; Lee Smolin

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The linearization of the Kodama state

Laurent Freidel, Lee Smolin

High Energy Physics - Theory · Submitted 23 Oct 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We find the answer is no in the Lorentzian theory.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.79	0.44	0.04	unclear 0.90
s1	We find the answer is no in the Lorentzian theory.	result 1.00	0.96	0.48	asserted 1.00
s2	However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable.	result 1.00	0.89	0.23	asserted 1.00
s3	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.	interpretation 0.98	0.55	0.06	unclear 0.72

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The paper

Original 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.

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References

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The Cosmological Constant from a Quantum Gravitational $\theta$-Vacua and the Gravitational Hall Effect
gr-qc 2025-06 conditional novelty 6.0 of 10

The cosmological constant is related to the topological theta angle by theta = 12 pi^2 / (Lambda l_Pl^2), suggesting Lambda is topologically protected.
Quantum Relaxation Dynamics of Vacuum Energy from Pre-Geometric Gravity
hep-th 2026-10 reject novelty 5.0 of 10

A pre-geometric gravity model is argued to quantize the cosmological constant into levels Λ_k ~ M_Pl^2/k, with an entropy-weighted tunneling rate driving the vacuum energy monotonically toward zero.
Loop Quantum Cosmology
gr-qc 2006-01 accept novelty 2.0 of 10

Loop quantum cosmology replaces the big bang singularity with a discrete difference equation whose solutions extend through the classically singular point, and this review lays out the effective equations and full-the...

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10 arXiv papers cite this in 15 sentences

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Papers citing it · 9 sentences without a confident label

Compares with it 1 paper

Let us take a moment to compare our approach to different works in LQG on gravitational waves.[ Several works not employing the Ashtekar formalism exist as well, see e.g. [ref] . ] Since we are working with states in the Hilbert space of full LQG, we differ from early approaches, where it was attempted to quantise only the linearised field theory [ref] .

Modifications to Gravitational Wave Equation from Canonical Quantum Gravity · Conclusion · 0.96

Cites it as support 1 paper

This has been substantiated in [ref] where it was shown that linearized perturbations around the Kodama state are non-normalizable under a linearized inner product.

In Search of Quantum de Sitter Space: Generalizing the Kodama State · The Problems · 0.99

Cites it as background 3 papers

The CSK state has long been an object of interest in canonical quantum gravity [ref] (see also [ref] for early open issues).

The Cosmological Constant from a Quantum Gravitational $\theta$-Vacua and the Gravitational Hall Effect · Introduction · 0.96
Particularly, in Loop Quantum Gravity (LQG) [ref] , there have been studies to understand the consequence of nonpertubative quantization in propagation of Gamma Ray Bursts (GRBs), other matter fields and GWs on cosmological or black holes spacetimes (for some examples see [ref] and the references within).

Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime · Introduction · 0.97
This state is known as the Kodama state [ref] .

Chern-Simons theory, Stokes' Theorem, and the Duflo map · Introduction · 0.92

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