Physics applications of asymptotically safe gravity

This article is about the applications of asymptotic safety. For a detailed introduction to asymptotic safety, see Asymptotic safety in quantum gravity.

The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties. For this reason it is possible that — assuming a particular set of couplings has been measured in an experiment — the requirement of asymptotic safety fixes all remaining couplings in such a way that the UV fixed point is approached.

Asymptotic safety, if realized in Nature, has far reaching consequences in all areas where quantum effects of gravity are to be expected. Their exploration, however, is still in its infancy. By now there are some phenomenological studies concerning the implications of asymptotic safety in particle physics, astrophysics and cosmology, for instance.

Asymptotic safety and the parameters of the Standard Model

The mass of the Higgs boson

The Standard Model in combination with asymptotic safety might be valid up to arbitrarily high energies. Based on the assumption that this is indeed correct it is possible to make a statement about the Higgs boson mass.^[1] The first concrete results were obtained by Shaposhnikov and Wetterich.^[2] Depending on the sign of the gravity induced anomalous dimension $A_{\lambda }$ there are two possibilities: For $A_{\lambda }<0$ the Higgs mass $m_{\text{H}}$ is restricted to the window $126\,{\text{GeV}}<m_{\text{H}}<174\,{\text{GeV}}$ . If, on the other hand, $A_{\lambda }>0$ which is the favored possibility, $m_{\text{H}}$ must take the value

m_{\text{H}}=126\,{\text{GeV}},

with an uncertainty of a few GeV only. In this spirit one can consider $m_{\text{H}}$ a prediction of asymptotic safety. The result is in surprisingly good agreement with the latest experimental data measured at CERN by the ATLAS and CMS collaborations.

The fine structure constant

By taking into account the gravitational correction to the running of the fine structure constant $\alpha$ of quantum electrodynamics, Harst and Reuter were able to study the impacts of asymptotic safety on the infrared (renormalized) value of $\alpha$ .^[3] They found two fixed points suitable for the asymptotic safety construction both of which imply a well-behaved UV limit, without running into a Landau pole type singularity. The first one is characterized by a vanishing $\alpha$ , and the infrared value $\alpha _{\text{IR}}$ is a free parameter. In the second case, however, the fixed point value of $\alpha$ is non-zero, and its infrared value is a computable prediction of the theory.

Asymptotic safety in astrophysics and cosmology

Phenomenological consequences of asymptotic safety can be expected also for astrophysics and cosmology. Bonanno and Reuter investigated the horizon structure of "renormalization group improved" black holes and computed quantum gravity corrections to the Hawking temperature and the corresponding thermodynamical entropy.^[4] By means of an RG improvement of the Einstein–Hilbert action, Reuter and Weyer obtained a modified version of the Einstein equations which in turn results in a modification of the Newtonian limit, providing a possible explanation for the observed flat galaxy rotation curves without having to postulate the presence of dark matter.^[5]

As for cosmology, Bonanno and Reuter argued that asymptotic safety modifies the very early Universe, possibly leading to a resolution to the horizon and flatness problem of standard cosmology.^[6] Furthermore, asymptotic safety provides the possibility of inflation without the need of an inflaton field (while driven by the cosmological constant).^[7] It was reasoned that the scale invariance related to the non-Gaussian fixed point underlying asymptotic safety is responsible for the near scale invariance of the primordial density perturbations. Using different methods, asymptotically safe inflation was analyzed further by Weinberg.^[8]

References

↑ Callaway, D.; Petronzio, R. (1987). "Is the standard model Higgs mass predictable?". Nuclear Physics B. 292: 497. Bibcode:1987NuPhB.292..497C. doi:10.1016/0550-3213(87)90657-2.
↑ Shaposhnikov, Mikhail; Wetterich, Christof (2010). "Asymptotic safety of gravity and the Higgs boson mass". Physics Letters B. 683 (2-3): 196–200. arXiv:0912.0208. Bibcode:2010PhLB..683..196S. doi:10.1016/j.physletb.2009.12.022.
↑ Harst, Ulrich; Reuter, Martin (2011). "QED coupled to QEG". Journal of High Energy Physics. 2011 (5): 119. arXiv:1101.6007. Bibcode:2011JHEP...05..119H. doi:10.1007/JHEP05(2011)119.
↑ Bonanno, Alfio; Reuter, Martin (2000). "Renormalization group improved black hole spacetimes". Physical Review D. 62 (4): 043008. arXiv:hep-th/0002196. Bibcode:2000PhRvD..62d3008B. doi:10.1103/PhysRevD.62.043008.
↑ Reuter, Martin; Weyer, Holger (2004). "Running Newton constant, improved gravitational actions, and galaxy rotation curves". Physical Review D. 70 (12): 124028. arXiv:hep-th/0410117. Bibcode:2004PhRvD..70l4028R. doi:10.1103/PhysRevD.70.124028.
↑ Bonanno, Alfio; Reuter, Martin (2002). "Cosmology of the Planck era from a renormalization group for quantum gravity". Physical Review D. 65 (4): 043508. arXiv:hep-th/0106133. Bibcode:2002PhRvD..65d3508B. doi:10.1103/PhysRevD.65.043508.
↑ Bonanno, Alfio; Reuter, Martin (2007). "Entropy signature of the running cosmological constant". Journal of Cosmology and Astroparticle Physics. 2007 (08): 024. arXiv:0706.0174. Bibcode:2007JCAP...08..024B. doi:10.1088/1475-7516/2007/08/024.
↑ Weinberg, Steven (2010). "Asymptotically safe inflation". Physical Review D. 81 (8): 083535. arXiv:0911.3165. Bibcode:2010PhRvD..81h3535W. doi:10.1103/PhysRevD.81.083535.

Theories of gravitation

Standard

Newtonian gravity (NG)	Newton's law of universal gravitation History of gravitational theory

General relativity (GR)	Introduction History Mathematics Resources Tests Post-Newtonian formalism Linearized gravity ADM formalism Gibbons–Hawking–York boundary term

Alternatives to
general relativity

Paradigms	Classical theories of gravitation Quantum gravity Theory of everything

Classical	Einstein–Cartan Bimetric theories Gauge theory gravity Teleparallelism Composite gravity f(R) gravity Massive gravity Modified Newtonian dynamics (MOND) Nonsymmetric gravitation Scalar–tensor theories Brans–Dicke Scalar–tensor–vector Conformal gravity Scalar theories Nordström Whitehead Geometrodynamics Induced gravity Tensor–vector–scalar Chameleon Pressuron

Quantisation	Euclidean quantum gravity Canonical quantum gravity Wheeler–DeWitt equation Loop quantum gravity Spin foam Causal dynamical triangulation Causal sets DGP model

Unification	Kaluza–Klein theory Dilaton Supergravity

Unification and quantisation	Noncommutative geometry Self-creation cosmology Semiclassical gravity Superfluid vacuum theory Logarithmic BEC vacuum String theory M-theory F-theory Heterotic string theory Type I string theory Type 0 string theory Bosonic string theory Type II string theory Little string theory Twistor theory Twistor string theory

Generalisations / Extensions of GR	Scale relativity Liouville gravity Lovelock theory (2+1)-dimensional topological gravity Gauss–Bonnet gravity Jackiw–Teitelboim gravity

Pre-Newtonian theories
and Toy models

Quantum gravity

Central concepts

Toy models

Quantum field theory
in curved spacetime

Black holes

Approaches

String theory	Bosonic string theory M-theory Supergravity Superstring theory

Canonical quantum gravity	Loop quantum gravity Wheeler–DeWitt equation

Euclidean quantum gravity	Hartle–Hawking state

Others	Causal dynamical triangulation Causal sets Noncommutative geometry Spin foam Group field theory Superfluid vacuum theory Twistor theory

Applications

Quantum cosmology

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