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Cited by 19Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesBlack Holes and Theoretical Physics

The DOI matches its Crossref record; 61 of the 61 references it cites were found in a registry or an index; none of the 18 sources its claims cite is checked for support yet.

Effect of the trace anomaly on the cosmological constant

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Koksma, Jurjen F., Prokopec, Tomislav·2008·Physical Review D
DOI 10.1103/physrevd.78.023508
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Abstract

It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this paper, however, we show by means of a semiclassical analysis that the trace anomaly does not affect the cosmological constant. We construct the effective action of the conformal anomaly for flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes consisting of local quadratic geometric curvature invariants. Counterterms are thus expected to influence the numerical value of the coefficients in the trace anomaly and we must therefore allow these parameters to vary. We calculate the evolution of the Hubble parameter in quasi-de Sitter spacetime, where we restrict our Hubble parameter to vary slowly in time, and in Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes. We show dynamically that a universe consisting of matter with a constant equation of state, a cosmological constant, and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. When considering the trace anomaly truncated to quasi-de Sitter spacetime, we find a region in parameter space where the quantum attractor destabilizes. When considering the exact expression of the trace anomaly, a stability analysis shows that whenever the trace anomaly driven attractor is stable, the classical de Sitter attractor is unstable, and vice versa. Semiclassically, the trace anomaly does not affect the classical late time de Sitter attractor, and hence it does not solve the cosmological constant problem.

Overview

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TL;DR

Using a semiclassical analysis, the authors show that the quantum trace anomaly does not affect the late-time effective cosmological constant; the classical de Sitter attractor is not dynamically altered. They derive the anomaly effective action in flat FLRW and find either classical or anomaly-driven attractors depending on parameters, but conclude the trace anomaly does not solve the cosmological constant problem.

Key findings

  • The trace anomaly can be generated by an infinite effective action in flat FLRW consisting of local quadratic curvature invariants \(R^2\) and the Gauss-Bonnet term \(E\); counterterms imply the coefficients \(b,b',b''\) are not uniquely fixed, so the authors vary them.
  • Late-time asymptotes are a classical de Sitter attractor \(H^0_C\) and a quantum anomaly-driven attractor \(H^0_A\), independent of \(b''\); in the small-\(\lambda\) expansion \(H^0_C \simeq \sqrt{\Lambda/3}[1-8\pi b'\lambda]\) and \(H^0_A \simeq \sqrt{-1/(16\pi G b')-\Lambda/3}\).
  • In quasi de Sitter spacetime, both attractors can be stable, but the quantum attractor destabilises when inequality (50) is violated; they illustrate this with \(b''=7b'/6<5b'/6\) for radiation \(w=1/3\), \(\lambda=1/50\), \(b'=-0.015\).
  • In exact FLRW spacetimes, stability depends on the sign of \(b''-2b'/3\): if \(>0\), the quantum attractor is stable and the classical de Sitter attractor is unstable; if \(<0\), the classical attractor is stable and the quantum attractor is unstable; at \(b''=2b'/3\), both are stable. The classical attractor shows under-damped oscillations, with frequency independent of the equation of state.

Methods

  • Semiclassical effective-field-theory approach: trace of the Einstein field equations plus stress-energy conservation, including matter with constant equation of state \(w>-1\), a cosmological constant, and the trace anomaly.
  • Derives the anomaly effective action in flat FLRW from local quadratic curvature invariants \(R^2\) and Gauss-Bonnet \(E\), then studies two regimes: quasi de Sitter spacetime with slowly varying \(H\) and truncated higher derivatives, and exact FLRW spacetime including all higher-derivative contributions via numerical and linear stability analysis.
  • Varies the anomaly coefficients \(b,b',b''\) because counterterms can shift their physical values; uses Standard Model values \(N_S=4\), \(N_F=45/2\), \(N_V=12\), with \(b'=-0.015\) and \(\lambda=1/50\) in figures.

Limitations

  • Stated: the authors do not consider a new conformal degree of freedom; they do not know whether the truncated quasi de Sitter or exact FLRW treatment is correct, and note that higher-derivative terms may destabilise the system (Ostrogradsky). The quantum attractor is of order the Planck mass, where perturbative general relativity may break down and quantum fluctuations may affect or remove it.
  • Stated: the physical coefficients in the trace anomaly have not been measured, so they must be allowed to vary.
  • Evident from the text: the analysis assumes flat, homogeneous, isotropic FLRW spacetimes and constant \(w>-1\); stability conclusions depend on the sign of \(b''-2b'/3\) and on \(\lambda\ll 1\).

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Crossref · 10.1103/physrevd.78.023508

Cites

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Citations

Cites

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Research works printed but not linked: 3

  1. 10.1007/s10714-007-0557-5 · DOI
  2. J. Donoghue, 1996, Helv. Phys. Acta, 69, 269
  3. I. L. Shapiro, Proc. Sci.

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Metadata

Authors
Koksma, J. F., & Prokopec, T.
Affiliations
Utrecht University (NL)
ORCID
Prokopec, Tomislav
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2008-07-08
Volume
78
Issue
2
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.78.023508
OpenAlex
W2166561590
Cited by
19
References
61
Citations by year
2025: 1 · 2023: 1 · 2021: 1 · 2020: 2 · 2019: 1 · 2017: 1 · 2015: 2 · 2014: 1 · 2013: 1
FWCI
1.15
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Universiteit Utrecht
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
trace anomaly, cosmological constant problem, Friedmann-Robertson-Walker spacetime, counterterms, Hubble parameter evolution, de Sitter attractor, attractor stability

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