Quantum linearization instabilities of de Sitter spacetime. I
Open accessAbstract
It is known that all the physical states in linearized gravity are required to be invariant under the continuous isometries of the background spacetime if it is spatially compact. For example, all the physical states in linearized gravity in de Sitter spacetime are required to be SO(4, 1) invariant. A detailed derivation of SO(4, 1) invariance of the physical state is presented. Also, it is found that normal ordering of operators is unnecessary in the constraints which demand SO(4, 1) invariance. Then it is proved that there are no normalizable SO(4, 1)-invariant states other than the vacuum state in the Fock space. This appears to suggest that there would be no dynamics in de Sitter spacetime. A step towards a possible resolution of this paradox will be presented in the sequel to this article.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The approach provides an overcomplete set of quantum observables, meaning a set whose classical counterparts are overcomplete on the constrained phase space.
“In the examples we will see that our approach in fact provides an 'overcomplete set' of quantum observables. By this we mean a set of observables whose classical counterparts are overcomplete (see. for example [13]) on the (constrained) phase space.”
From Quantum observables and recollapsing dynamics (1995) · cites this paper as [13]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Cosmological event horizons, thermodynamics, and particle creation
Gibbons, G. W., & Hawking, S. W. (1977) · Physical Review D · doi:10.1103/physrevd.15.2738 · Cited by 3,192 · see citing works
Vacuum states in de Sitter space
Allen, B. (1985) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.32.3136 · Cited by 797 · see citing works
Space–time symmetries and linearization stability of the Einstein equations. II
Moncrief, V. (1976) · Journal of Mathematical Physics · doi:10.1063/1.522814 · Cited by 205 · see citing works
Spacetime symmetries and linearization stability of the Einstein equations. I
Moncrief, V. (1975) · Journal of Mathematical Physics · doi:10.1063/1.522572 · Cited by 192 · see citing works
Symmetry and bifurcations of momentum mappings
Arms, J. M., Marsden, J. E., & Moncrief, V. (1981) · Communications in Mathematical Physics · doi:10.1007/bf02046759 · Cited by 187 · see citing works
Restoration of spontaneously broken continuous symmetries in de Sitter spacetime
Ratra, B. (1985) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.31.1931 · Cited by 150 · see citing works
Quantum linearization instabilities of de Sitter spacetime. II
Higuchi, A. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/11/010 · Cited by 128 · see citing works
Self-citationArms, J. M., Marsden, J. E., & Moncrief, V. (1982) · Annals of Physics · doi:10.1016/0003-4916(82)90105-1 · Cited by 106 · see citing works
Instability of closed spaces in general relativity
Brill, D. R., & Deser, S. (1973) · Communications in Mathematical Physics · doi:10.1007/bf01645610 · Cited by 105 · see citing works
Linearization stability of the Einstein equations
Fischer, A. E., & Marsden, J. E. (1973) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1973-13299-9 · Cited by 103 · see citing works
Linearized gravity in de Sitter spacetime as a representation of SO(4, 1)
Higuchi, A. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/11/011 · Cited by 54 · see citing works
Self-citationInvariant states and quantized gravitational perturbations
Moncrief, V. (1978) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.18.983 · Cited by 47 · see citing works
Burges, C. J. C. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90562-5 · Cited by 40 · see citing works
Quantum linearization instabilities
Moncrief, V. (1979) · General Relativity and Gravitation · doi:10.1007/bf00756792 · Cited by 26 · see citing works
Excited-state spectra of de Sitter-space scalar fields
Redmount, I. H. (1989) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.40.3343 · Cited by 14 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Misner C W , Thorne K S and Wheeler J A 1973 Grovitofion (San Francisco: Freeman) Moncrief V 1986 private communication ed L Witten (New York: Wiley)
Cited by
Sorted by citations
An algebra of observables for de Sitter space
Chandrasekaran, V., Longo, R., Penington, G., & Witten, E. (2023) · Journal of High Energy Physics · doi:10.1007/jhep02(2023)082 · Cited by 290 · see citing works
Infrared effects in inflationary correlation functions
Seery, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/12/124005 · Cited by 200 · see citing works
Quantum observables and recollapsing dynamics
Marolf, D. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/5/011 · Cited by 153 · see citing works
Quantum linearization instabilities of de Sitter spacetime. II
Higuchi, A. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/11/010 · Cited by 128 · see citing works
Self-citationInfrared effects in inflationary correlation functions
Seery, D. (2010) · Figshare · Cited by 101 · see citing works
de Sitter invariance of the dS graviton vacuum
Higuchi, A., Marolf, D. M., & Morrison, I. A. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/24/245012 · Cited by 81 · see citing works
Self-citationAlmost ideal clocks in quantum cosmology: a brief derivation of time
Marolf, D. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/10/007 · Cited by 77 · see citing works
Comparing formulations of generalized quantum mechanics for reparametrization-invariant systems
Hartle, J. B., & Marolf, D. M. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.56.6247 · Cited by 72 · see citing works
Higher spin de Sitter Hilbert space
Anninos, D., Frederik Denef, B., Monten, R., & Sun, Z. (2019) · Journal of High Energy Physics · doi:10.1007/jhep10(2019)071 · Cited by 70 · see citing works
Group averaging for de Sitter free fields
Marolf, D. M., & Morrison, I. A. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/23/235003 · Cited by 66 · see citing works
A global picture of quantum de Sitter space
Giddings, S. B., & Marolf, D. M. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.064023 · Cited by 61 · see citing works
Almost ideal clocks in quantum cosmology: a brief derivation of time
Marolf, D. M. (1994) · CERN Document Server (European Organization for Nuclear Research) · Cited by 56 · see citing works
Linearized gravity in de Sitter spacetime as a representation of SO(4, 1)
Higuchi, A. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/11/011 · Cited by 54 · see citing works
Self-citationPath integrals and instantons in quantum gravity: Minisuperspace models
Marolf, D. M. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.6979 · Cited by 49 · see citing works
Cosmological Perturbation Theory in Slow-Roll Spacetimes
Losic, B., & Unruh, W. G. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.111101 · Cited by 51 · see citing works
Scalar field instability in de Sitter space–time
Dolgov, A. D., & Pelliccia, D. N. (2005) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2005.12.002 · Cited by 50 · see citing works
Infrared effects in a de Sitter background
Dolgov, A. D., Einhorn, M. B., & Zakharov, V. I. (1995) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.52.717 · Cited by 49 · see citing works
Higuchi, A. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/7/072001 · Cited by 41 · see citing works
Self-citationLeading order gravitational backreactions in de Sitter spacetime
Losic, B., & Unruh, W. G. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.74.023511 · Cited by 40 · see citing works
The Hilbert space of de Sitter quantum gravity
Chakraborty, T., Chakravarty, J., Godet, V., Paul, P., & Raju, S. (2024) · Journal of High Energy Physics · doi:10.1007/jhep01(2024)132 · Cited by 38 · see citing works
Krein space quantization in curved and flat spacetimes
Garidi, T., Huguet, E., & Renaud, J. (2004) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/1/018 · Cited by 27 · see citing works
Holography of information in de Sitter space
Chakraborty, T., Chakravarty, J., Godet, V., Paul, P., & Raju, S. (2023) · Journal of High Energy Physics · doi:10.1007/jhep12(2023)120 · Cited by 29 · see citing works
The discreet charm of the discrete series in dS2
Anninos, D., Anous, T., Pethybridge, B., & Şengör, G. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad14ad · Cited by 25 · see citing works
Crossed products, conditional expectations and constraint quantization
Klinger, M. S., & Leigh, R. G. (2024) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2024.116622 · Cited by 18 · see citing works
Nakamura, K. (2013) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptt006 · Cited by 17 · see citing works
Group averaging of massless scalar fields in 1 + 1 de Sitter
Marolf, D. M., & Morrison, I. A. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/3/035001 · Cited by 16 · see citing works
Foliation-based quantization and black hole information
Park, I. Y. (2017) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aa9602 · Cited by 16 · see citing works
Four-Dimensional Covariance of Feynman Diagrams in Einstein Gravity
Park, I. Y. (2018) · Theoretical and Mathematical Physics · doi:10.1134/s0040577918050094 · Cited by 16 · see citing works
Foliation-Based Approach to Quantum Gravity and Applications to Astrophysics
Park, I. (2019) · Universe · doi:10.3390/universe5030071 · Cited by 16 · see citing works
Allen, B., Caldwell, R. R., & Koranda, S. (1995) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.51.1553 · Cited by 14 · see citing works
Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
Vuyst, J. D., Eccles, S., Höhn, P. A., & Kirklin, J. (2025) · Journal of High Energy Physics · doi:10.1007/jhep07(2025)063 · Cited by 19 · see citing works
Reduction of gravity-matter and dS gravity to hypersurface
Park, I. Y. (2017) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s021988781750092x · Cited by 13 · see citing works
Absolute entropy and the observer’s no-boundary state
Blommaert, A., Kudler-Flam, J., & Urbach, E. Y. (2025) · Journal of High Energy Physics · doi:10.1007/jhep11(2025)113 · Cited by 15 · see citing works
Ahmad, S. A., Chemissany, W. A., Klinger, M. S., & Leigh, R. G. (2025) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2025.116911 · Cited by 14 · see citing works
De Sitter quantum gravity and the emergence of local algebras
Kaplan, M., Marolf, D. M., Yu, X., & Zhao, Y. (2025) · Journal of High Energy Physics · doi:10.1007/jhep04(2025)171 · Cited by 12 · see citing works
Linear instability of nonvacuum spacetimes
Kastor, D. A., & Traschen, J. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.47.480 · Cited by 11 · see citing works
Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
Pejhan, H., Enayati, M., Gazeau, J., & Wang, A. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.066012 · Cited by 10 · see citing works
Aspects of nonlinear perturbations in cosmological models
Unruh, W. G., & Losic, B. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/15/154012 · Cited by 8 · see citing works
Linearization (in)stabilities and crossed products
Vuyst, J. D., Eccles, S., Höhn, P. A., & Kirklin, J. (2025) · Journal of High Energy Physics · doi:10.1007/jhep05(2025)211 · Cited by 7 · see citing works
Observer dependence in quantum cosmology
Calzetta, E., & Kandus, A. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.48.3906 · Cited by 6 · see citing works
Quantization of Gravity and Finite Temperature Effects
Park, I. Y. (2021) · Particles · doi:10.3390/particles4040035 · Cited by 5 · see citing works
Unitary rigid supersymmetry for the chiral graviton and chiral gravitino in de Sitter spacetime
Higuchi, A., & Letsios, V. A. (2025) · Journal of High Energy Physics · doi:10.1007/jhep12(2025)104 · Cited by 4 · see citing works
Self-citationPhoton propagator for inflation in the general covariant gauge
Domazet, S., Glavan, D., & Prokopec, T. (2024) · Journal of High Energy Physics · doi:10.1007/jhep07(2024)103 · Cited by 4 · see citing works
Constraint rescaling in refined algebraic quantisation: Momentum constraint
Louko, J., & Martínez-Pascual, E. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3664336 · Cited by 4 · see citing works
Fluctuation theorems, quantum channels and gravitational algebras
Cirafici, M. (2024) · Journal of High Energy Physics · doi:10.1007/jhep11(2024)089 · Cited by 4 · see citing works
“Black universe” epoch in string cosmology
Buchel, A., & Kofman, L. A. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.086002 · Cited by 4 · see citing works
Cotler, J. S., & Jensen, K. (2026) · Journal of High Energy Physics · doi:10.1007/jhep03(2026)180 · Cited by 3 · see citing works
Gibbons, J., Higuchi, A., & Lima, W. C. C. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.065016 · Cited by 3 · see citing works
Self-citationPhoton quantization in cosmological spaces
Glavan, D. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.085014 · Cited by 3 · see citing works
Dynamics of backreactions around pure de Sitter spacetime
Losic, B. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/25/s45 · Cited by 3 · see citing works
Constraint rescaling in refined algebraic quantisation: momentum constraintPreprint
Louko, J. (2011) · Cited by 3 · see citing works
Gravitational Algebras and Applications to Nonequilibrium Physics
Cirafici, M. (2025) · Universe · doi:10.3390/universe11010024 · Cited by 1 · see citing works
Cosmological correlators in gravitationally-constrained de Sitter states
Chakraborty, T., Ashik, H., & Raju, S. (2026) · Journal of High Energy Physics · doi:10.1007/jhep01(2026)004 · Cited by 1 · see citing works
What is a photon in de Sitter spacetime?
Loparco, M., Penedones, J., & Ulrich, Y. (2026) · Journal of High Energy Physics · doi:10.1007/jhep02(2026)220 · Cited by 1 · see citing works
Anninos, D., Baracco, C., Letsios, V. A., & Mühlmann, B. (2026) · Journal of High Energy Physics · doi:10.1007/jhep07(2026)178 · Cited by 1 · see citing works
Black Hole Entropy from Non-dirichlet Sectors, and a Bounce Solution
Park, I. Y. (2023) · Foundations of Physics · doi:10.1007/s10701-023-00719-5 · Cited by 1 · see citing works
Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
Martínez-Pascual, E. (2013) · Journal of Mathematical Physics · doi:10.1063/1.4817485 · Cited by 1 · see citing works
SO(4)-invariant states in quantum cosmology
Fay Dowker, B. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/8/006 · Cited by 1 · see citing works
The eigenmodes for spinor quantum field theory in global de Sitter space–time
Letsios, V. A. (2021) · Journal of Mathematical Physics · doi:10.1063/5.0038651 · Cited by 15 · see citing works
Linearized gravity in “closed” universes with continuous symmetries
Higuchi, A. (2008) · Springer eBooks · doi:10.1007/3-540-59163-x_284
Self-citationOn 4D covariance of Feynman diagrams of Einstein gravity
Пак, И. Ё., & Park, I. Y. (2018) · Теоретическая и математическая физика · doi:10.4213/tmf9404
Supergravity on a three-torus: quantum linearization instabilities with a supergroup
Higuchi, A., & Schmieding, L. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab90a4
Self-citationFrom von Neumann algebras to quantum de Sitter
Fiol, B. (2023) · Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU) · doi:10.22323/1.436.0133
The (no) boundary proposal and excited states in de Sitter holography
Cantcheff, M. B., Cruz, F. L., & Martínez, P. J. (2025) · Journal of High Energy Physics · doi:10.1007/jhep09(2025)173
Quantum Physics in de Sitter Spacetime
Anninos, D. (2026) · doi:10.1093/9780197851753.003.0161
- Authors
- Higuchi, A.
- Affiliations
- University of Maryland, College Park (US)
- Corresponding author
- Higuchi, A
- ORCID
- Higuchi, A
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1991-11-01
- Volume
- 8
- Issue
- 11
- Pages
- 1961-1981
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W4237561863
- Cited by
- 66
- References
- 15
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 5 · 2023: 5 · 2021: 4 · 2020: 1 · 2019: 3 · 2018: 2 · 2017: 2 · 2013: 2
- FWCI
- 1.91
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Funders
- National Science Foundation (8716803)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- de Sitter space, linearized gravity, isometries, normalizability, Fock space, vacuum state, normal ordering, dynamical spacetime
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
