Special Issue "Modified Theories of Gravity"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 January 2020.

Special Issue Editor

Prof. Stephon Alexander
E-Mail Website
Guest Editor
Professor of Physics, Brown University, Providence, RI, USA, President Elect
Interests: theoretical cosmology; cosmological constant problem; baryogenesis; cosmic inflation; structure formation; singularity resolution; quantum fields in curved spaces; string cosmology; quantum gravity; string theory; modified theories of gravity; loop quantum gravity; spin foams; geometry and math of music; instrument acoustic modelling

Special Issue Information

Dear Colleagues,

Einstein’s theory of general relativity has seen tremendous experimental success over the last century, most recently with the observation of gravitational waves. However, a handful of observations, such as dark matter, dark energy and black holes motivate the construction of theories that go beyond general relativity. Also, we still lack a complete theory of the early universe free of singularities, which also motivate modified theories of gravity that address these issues. Finally, modified theories of gravity arise naturally in the semiclassical limit of some quantum theories of gravity such as string theory and loop quantum gravity. Conversely, modified theories of gravity can motivate the correct starting point for quantizing gravity. This Special Issue will explore all of these dimensions of modified theories of gravity.

Prof. Stephon Alexander
Guest Editor

Manuscript Submission Information

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Keywords

  • modified theories of gravity
  • loop quantum gravity
  • string theory
  • dark matter
  • dark energy
  • black holes

Published Papers (5 papers)

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Research

Open AccessArticle
Renormalizable and Unitary Model of Quantum Gravity
Symmetry 2019, 11(11), 1334; https://doi.org/10.3390/sym11111334 - 25 Oct 2019
Abstract
We consider R+R2 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)
Open AccessArticle
Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole
Symmetry 2019, 11(10), 1303; https://doi.org/10.3390/sym11101303 - 16 Oct 2019
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)
Open AccessArticle
Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole
Symmetry 2019, 11(10), 1294; https://doi.org/10.3390/sym11101294 - 15 Oct 2019
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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Open AccessArticle
The Quantum Cosmological Constant
Symmetry 2019, 11(9), 1130; https://doi.org/10.3390/sym11091130 - 05 Sep 2019
Cited by 3
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)
Open AccessArticle
Applications of Canonical Quantum Gravity to Cosmology
Symmetry 2019, 11(8), 1005; https://doi.org/10.3390/sym11081005 - 03 Aug 2019
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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