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Cited by 18Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical Physics

The DOI matches its Crossref record; 117 of the 118 references it cites were found in a registry or an index; none of the 28 sources its claims cite is checked for support yet.

Instability of de Sitter spacetime induced by quantum conformal anomaly

Open access
Matsui, Hiroki·2019·Journal of Cosmology and Astroparticle Physics
DOI 10.1088/1475-7516/2019/01/003
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Abstract

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.

Overview

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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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Integrity signals

Registry

Crossref · 10.1088/1475-7516/2019/01/003

Cites

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Citations

Cites

Research works printed but not linked: 3

  1. A.A. Starobinsky, 1979, 30, 682
  2. A.H. Guth, 2007, J. Phys., 40, 6811
  3. P.J. Steinhardt, 1983, Natural inflation, in Very early universe

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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)
DOI
10.1088/1475-7516/2019/01/003
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
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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