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8 pages, 280 KiB

Open AccessArticle

Resummed Quantum Gravity: A Review with Applications

by B. F. L. Ward

Symmetry 2021, 13(7), 1304; https://doi.org/10.3390/sym13071304 - 20 Jul 2021

Viewed by 1967

We summarize the status of the theory of resummed quantum gravity. In the context of the Planck scale cosmology formulation of Bonanno and Reuter, we review the use of our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the [...] Read more.

We summarize the status of the theory of resummed quantum gravity. In the context of the Planck scale cosmology formulation of Bonanno and Reuter, we review the use of our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as

ρ_{Λ}

= (0.0024 eV)

^{4}

. Constraints on susy GUT models that follow from the closeness of the estimate to experiment are noted. Various consistency checks on the calculation are discussed. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of

ρ_{Λ}

. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

15 pages, 1420 KiB

Open AccessArticle

Dark Matter as a Result of Field Oscillations in the Modified Theory of Induced Gravity

by Farkhat Zaripov

Symmetry 2020, 12(1), 41; https://doi.org/10.3390/sym12010041 - 24 Dec 2019

Cited by 2 | Viewed by 2743

Abstract

The paper studies the modified theory of induced gravity (MTIG). The solutions of the MTIG equations contain two branches (stages): Einstein (ES) and “restructuring” (RS). Previously, solutions were found that the values of such parameters as the “Hubble parameter”, gravitational and cosmological “constants” [...] Read more.

The paper studies the modified theory of induced gravity (MTIG). The solutions of the MTIG equations contain two branches (stages): Einstein (ES) and “restructuring” (RS). Previously, solutions were found that the values of such parameters as the “Hubble parameter”, gravitational and cosmological “constants” at the RS stage, fluctuate near monotonously developing mean values. This article gives MTIG equations with arbitrary potential. Solutions of the equations of geodesic curves are investigated for the case of centrally symmetric space and quadratic potential at the RS stage. The oscillatory nature of the solutions leads to the appearance of a gravitational potential containing a spectrum of minima, as well as to antigravity, which is expressed by acceleration directed from the center. Such solutions lead to the distribution of the potential of the gravitational field creating an additional mass effect at large distances and are well suited for modeling the effect of dark matter in galaxies. The solutions of the equation of geodesic lines are obtained and analyzed. We found that the transition from flat asymptotics to oscillatory asymptotics at large distances from the center with a combination of the presence of antigravity zones leads to a rich variety of shapes and dynamics of geodesic curves and to the formation of complex structures. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

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11 pages, 323 KiB

Open AccessArticle

Constraints on the String T-Duality Propagator from the Hydrogen Atom

by Michael F. Wondrak and Marcus Bleicher

Symmetry 2019, 11(12), 1478; https://doi.org/10.3390/sym11121478 - 4 Dec 2019

Cited by 5 | Viewed by 2200

Abstract

We investigated the implications of string theory in the high-precision regime of quantum mechanics. In particular, we examined a quantum field theoretical propagator which was derived from string theory when compactified at the T-duality self-dual radius and which is closely related to the [...] Read more.

We investigated the implications of string theory in the high-precision regime of quantum mechanics. In particular, we examined a quantum field theoretical propagator which was derived from string theory when compactified at the T-duality self-dual radius and which is closely related to the path integral duality. Our focus was on the hydrogen ground state energy and the

1 S_{1 / 2} - 2 S_{1 / 2}

transition frequency, as they are the most precisely explored properties of the hydrogen atom. The T-duality propagator alters the photon field dynamics leading to a modified Coulomb potential. Thus, our study is complementary to investigations where the electron evolution is modified, as in studies of a minimal length in the context of the generalized uncertainty principle. The first manifestation of the T-duality propagator arises at fourth order in the fine-structure constant, including a logarithmic term. For the first time, constraints on the underlying parameter, the zero-point length, are presented. They reach down to

3.9 \times 10^{- 19} m

and are in full agreement with previous studies on black holes. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

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8 pages, 232 KiB

Open AccessArticle

Renormalizable and Unitary Model of Quantum Gravity

by S. A. Larin

Symmetry 2019, 11(11), 1334; https://doi.org/10.3390/sym11111334 - 25 Oct 2019

Cited by 3 | Viewed by 2865

Abstract

We consider

R + R^{2}

relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, [...] Read more.

We consider

R + R^{2}

relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the

R + R^{2}

model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the

R + R^{2}

Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the

R + R^{2}

model is a good candidate for the fundamental quantum theory of gravity. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

16 pages, 308 KiB

Open AccessArticle

Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole

by A. J. Nurmagambetov and I. Y. Park

Symmetry 2019, 11(10), 1303; https://doi.org/10.3390/sym11101303 - 16 Oct 2019

Cited by 7 | Viewed by 2122

Abstract

We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, [...] Read more.

We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, the analysis is extended to a rotating black hole solution of an Einstein–Maxwell-scalar system with a Higgs potential. Although the analysis becomes much more complex compared to that of the previous, we observe the same basic features, including the quantum-gravitational trans-Planckian energy near the horizon. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

16 pages, 898 KiB

Open AccessArticle

Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole

by Meir Lewkowicz and Mikhail Zubkov

Symmetry 2019, 11(10), 1294; https://doi.org/10.3390/sym11101294 - 15 Oct 2019

Cited by 6 | Viewed by 2014

Abstract

We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed [...] Read more.

We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of ordinary general relativity. Next, we consider the motion of particles in the presence of a black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

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11 pages, 265 KiB

Open AccessEditor’s ChoiceArticle

The Quantum Cosmological Constant

by Stephon Alexander, Joao Magueijo and Lee Smolin

Symmetry 2019, 11(9), 1130; https://doi.org/10.3390/sym11091130 - 5 Sep 2019

Cited by 24 | Viewed by 3114

Abstract

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time [...] Read more.

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

15 pages, 290 KiB

Open AccessArticle

Applications of Canonical Quantum Gravity to Cosmology

by Claus Gerhardt

Symmetry 2019, 11(8), 1005; https://doi.org/10.3390/sym11081005 - 3 Aug 2019

Cited by 1 | Viewed by 2659

Abstract

We applied quantum gravitational results to spatially unbounded Friedmann universes and tried to answer some questions related to dark energy, dark matter, inflation, and the missing antimatter. Full article

(This article belongs to the Special Issue Modified Theories of Gravity)

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