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Instability of de Sitter spacetime induced by quantum conformal anomaly
Open accessAbstract
The instability of (quasi) de Sitter spacetime from quantum gravitational effects has been discussed in many works. Especially, the gravitational backreaction from quantum energy momentum tensor is crucial for understanding the low-energy description of quantum gravity and sometimes destabilize the spacetime. In this paper we discuss the (quasi) de Sitter instability from gravitational backreaction involving quantum conformal anomaly. The conformal or trace anomaly corresponds to the quantum gravitational contributions of the massless conformal fields and affects the spacetime homogeneously. First, we derive the conformal anomaly using the adiabatic (WKB) approximation and discuss the renormalization of the quantum energy momentum tensor. Then, we consider the dynamics of the Hubble parameter based on the semiclassical Einstein's equations including the cosmological constant, the conformal anomaly and the higher-derivative terms. We have clearly shown that the classical de Sitter attractor H C ≃ √Λ/3 are generally unstable from the viewpoint of the semiclassical gravity and the inflation is destabilized except for the specific conditions. Unless the fine-tuning of the conformal anomaly and the higher derivative terms, the inflation finally becomes the Planckian inflation with the Hubble scale H ≈ M P ≡ √1/8π G N or terminates H ( t ) → 0. The latter case suggests that the cosmic inflation could not last long and the eternal inflation scenarios are strongly constrained.
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TL;DR
The paper argues that semiclassical backreaction from the quantum conformal anomaly generically destabilizes (quasi-)de Sitter spacetime, so the classical de Sitter attractor \(H_C \sim \sqrt{\Lambda/3}\) survives only under fine-tuned conditions. Unless the anomaly and higher-derivative terms are tuned, inflation either runs to the Planckian scale \(H \approx M_P\) or terminates with \(H(t)\to 0\), constraining eternal inflation.
Key findings
- Deriving the conformal anomaly via the adiabatic (WKB) approximation for conformally coupled fields gives \(T^\mu_{\ \mu\,\text{anomaly}} = \frac{1}{360(4\pi)^2}E - \frac{1}{180(4\pi)^2}R\), consistent with dimensional-regularization effective-action results; the adiabatic vacuum \(|0_A\rangle\) is argued to remove the \(R\)-term ambiguity.
- The semiclassical equations yield two attractors: the classical \(H_C \sim \sqrt{\Lambda/3}\) and a quantum anomaly-driven \(H_Q \sim M_P/\sqrt{2b}\). The classical de Sitter solution’s stability depends on the sign of \(c\), with \(c>0\) requiring \(N_G > \frac{1}{18}N_S + \frac{1}{3}N_F\).
- For \(c<0\) and \(H(t_0)\ll \sqrt{\Lambda}\), de Sitter is destabilized and \(H(t)\to 0\); for \(c<0\) and \(H(t_0)\gg \sqrt{\Lambda}\), \(H(t)\to M_P/\sqrt{2b}\); for \(c>0\) and \(H(t_0)\ll \sqrt{\Lambda}\), \(H(t)\to\infty\); for \(c>0\) and \(\sqrt{\Lambda}\ll H(t_0)\ll M_P/\sqrt{2b}\), \(H(t)\to\sqrt{\Lambda/3}\).
- Including higher-derivative terms, the stability condition is \(\Lambda \ll H(t_0) \ll M_P\sqrt{b-a_2/8+a_3/2}\) and \(c+6a_1-a_2/4>0\); otherwise inflation cannot last long. Eternal old, new, and chaotic inflation are constrained: \(H(t)\to 0\) terminates inflation, while \(H(t)\to M_P\) leaves the final state dependent on the potential.
Methods
- Semiclassical gravity: matter fields are quantized on a classical flat FLRW metric; a conformally coupled scalar field is decomposed into modes, and the adiabatic (WKB) approximation with the adiabatic vacuum is used to renormalize the stress tensor and derive the conformal anomaly.
- Effective Einstein equations include the cosmological constant, conformal anomaly, and higher-derivative tensors \(H^{(1,2,3)}_{\mu\nu}\); these are reduced to first-order Hubble-flow equations and numerically solved as phase diagrams for MSSM-like (\(b=8/45\pi^2\), \(c=-1/36\pi^2\)) and SM-like (\(b=11/72\pi^2\), \(c=17/720\pi^2\)) particle contents.
- Cosmological implications for eternal old, new, and chaotic inflation are discussed using Coleman-de Luccia/Hawking-Moss vacuum decay and stochastic inflationary fluctuation arguments.
Limitations
- Stated: the one-loop anomaly description is valid while \(R_{\mu\nu\kappa\lambda}R^{\mu\nu\kappa\lambda}\ll M_P^4\); otherwise higher-loop matter or graviton corrections cannot be neglected. The paper notes the one-loop expression is exact in theories such as \(N=4\) SYM.
- Stated: gravitational derivative couplings \(a_{1,2,3}\) are dropped for simplicity in the initial analysis and later included; the stability summary assumes \(\dot H(t_0)=0\) for simplicity. Gauge dependence of the \(R\) term for gauge fields is said to be removable by gravitational couplings.
- Evident from the text: the numerical phase diagrams and stability conclusions depend on chosen particle content and unfixed parameters \(b,c,a_{1,2,3}\); the paper does not provide observational constraints on those parameters.
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35 Own interpretation · 29 Own result · 7 No full text of the sources · 4 Check pending · 4 Not checked yet · 2 Own method · 2 No basis given · 1 Sources not found
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In the paper
“The first part originates from the lowest-order adiabatic term of T 00 which is renormalized by the cosmological constant term ρ Λ .”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“On the other hand the adiabatic regularization leads to the wrong sign of the conformal anomaly [72].”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
What the sources say
- Check pendingcites [72] T.S. Bunch, 1980, J. Phys. source
plainstates a cause- Asserted: passes — The authors put it forward as true.
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In the paper
“Note that eq.(2.30) is consistent with the results from the effective action Γ eff [g µν ] of gravity [6] in the dimensional regularization.”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
What the sources say
- Not checked — no full text of the sourcecites [6] I.L. Buchbinder, 1992, Effective action in quantum gravity source
plainstates an association- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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In the paper
“Now, we point out that the adiabatic expressions for the conformal anomaly precisely matches the expression derived by the effective action Γ eff [g µν ] with the dimensional regularization [6].”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
What the sources say
- Not checked — no full text of the sourcecites [6] I.L. Buchbinder, 1992, Effective action in quantum gravity source
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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A result the paper states — it cites no source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For massless conformal coupled fields there is no quantum particle creation with respect to the adiabatic vacuum |0 A .”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
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In the paper
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > Additional information
“Most of the Hubble patches ends the inflation and begins the reheating.”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > Additional information
“Most of the Hubble patches of the universe are still during the inflation and the whole universe is eternally expanding.”
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In the paper
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
“N G abelian gauge (spin-1) fields.”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
“Finally, the massless particle in current universe is only photon, thus, N V = 1, N S = 0 and N G = 0.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
“T µ µ fermion anomaly = - 1 2880π 2 11 R µν R µν - 1 3 R 2 + 6 R = 11 360(4π) 2 E - 6 180(4π) 2 R.”
§ Instability of de Sitter spacetime induced by quantum conformal anomaly > JCAP01(2019)003
“b = 1 360(4π) 2 N S + 11 2 N F + 62N G , (3.3b)”
Citations
Cites
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106 · cited 1×
“Especially, including backreaction effects of the quantum fluctuations onto the spacetime is crucial for understanding the quantum nature of the gravity and the evaporation of the back hole [5].”
BackgroundInflationary universe: A possible solution to the horizon and flatness problems
Guth, A. H. (1981) · Physical Review D · doi:10.1103/physrevd.23.347 · Cited by 9,983
Quantum Fields in Curved Space
Birrell, N. D., & Davies, P. C. W. (1982) · doi:10.1017/cbo9780511622632 · Cited by 8,354
A new type of isotropic cosmological models without singularity
Starobinsky, A. A. (1980) · Physics Letters B · doi:10.1016/0370-2693(80)90670-x · Cited by 7,677
Linde, A. D. (1982) · Physics Letters B · doi:10.1016/0370-2693(82)91219-9 · Cited by 6,405
Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking
Albrecht, A., & Steinhardt, P. J. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1220 · Cited by 4,981
de Sitter vacua in string theory
Shamit Kachru, A., Каллош, Р., Linde, A. D., & Trivedi, S. P. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.68.046005 · Cited by 3,816
Cosmological constant—the weight of the vacuum
Padmanabhan, T. (2003) · Physics Reports · doi:10.1016/s0370-1573(03)00120-0 · Cited by 3,212
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
Cosmological Constant - the Weight of the VacuumPreprint
Padmanabhan, Τ. (2002) · Cited by 2,145
Research works printed but not linked: 3
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- A.H. Guth, 2007, J. Phys., 40, 6811
- P.J. Steinhardt, 1983, Natural inflation, in Very early universe
Cited by
Eternal inflation and swampland conjectures
Matsui, H., & Takahashi, F. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.023533 · Cited by 99
Self-citationEichhorn, A., Hebecker, A., Pawlowski, J. M., & Walcher, J. (2024) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/ada1f3 · Cited by 23
De Sitter quantum breaking, swampland conjectures and thermal strings
Blumenhagen, R., Kneißl, C., & Makridou, A. (2021) · Journal of High Energy Physics · doi:10.1007/jhep10(2021)157 · Cited by 17
Halim, A. A., Abreu, P., Aglietta, M., Allekotte, I., Cheminant, K. A., Almela, A., Aloisio, R., Álvarez-Muñiz, J., Yebra, J. A., Anastasi, G. A., et al. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.l081101 · Cited by 13
Quantum (in)stability of maximally symmetric space-times
Ghosh, J. K., KIRITSIS, E. B., Nitti, F., & Nourry, V. (2023) · Journal of High Energy Physics · doi:10.1007/jhep11(2023)098 · Cited by 12
Metadata
- Authors
- Matsui, H.
- Affiliations
- Tohoku University (JP)
- Corresponding author
- Matsui, Hiroki
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2019-01-03
- Volume
- 2019
- Issue
- 01
- Pages
- 003-003
- ISSN
- 1475-7516 (ISSN-L)
- OpenAlex
- W2908487400
- Cited by
- 18
- References
- 118
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 2 · 2020: 1 · 2019: 5
- FWCI
- 1.02
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science (17H02875)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- de Sitter instability, trace anomaly, gravitational backreaction, semiclassical gravity, cosmological constant, higher-derivative gravity, inflation (cosmology), eternal inflation, renormalization
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