Higher-Derivative Theories of Gravity

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Gravitation".

Deadline for manuscript submissions: closed (15 July 2022) | Viewed by 5594

Special Issue Editors

NORDITA, Hannes Alfvéns väg 12, 114 19 Stockholm, Sweden
Interests: general relativity; quantum gravity; higher-derivative gravity; nonlocal quantum field theory; black holes; gravitational waves
Special Issues, Collections and Topics in MDPI journals
Dipartimento di Fisica “E.R Caianiello”, Università degli Studi di Salerno, Via Giovanni Paolo II, 132 - 84084 Fisciano (SA), Italy
Interests: extended theories of gravity; higher derivative and nonlocal field theories; quantum field theory in curved spacetime; cosmology; astro-particle physics; neutrino physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

A vast amount of observational data have made Einstein's General Relativity (GR) the best current theory that describes classical aspects of the gravitational interaction. However, despite its great success, there are still fundamental questions that remain unanswered. On short-distance scales, GR predicts the existence of black-hole and cosmological big-bang singularities where spacetime terminates and the theory breaks down. Moreover, Einstein's theory lacks predictability in the high-energy regime, being perturbatively non-renormalizable.

A natural way to extend GR in the high-energy and short-distance regimes is to generalize the Einstein–Hilbert Lagrangian by adding higher powers of the curvature tensors. Indeed, in 1977, Kellogg Stelle showed that quadratic curvatures are sufficient to formulate a renormalizable theory of quantum gravity. However, such additional terms were also shown to introduce a “ghost” degree of freedom because of higher-order time-derivatives that cause classical Hamiltonian instabilities and break unitarity at the quantum level. This moment in the history of Theoretical Physics—more than forty years ago—can be considered to be the beginning of many new attempts aimed at formulating a consistent quantum theory of gravity, and thus at solving both issues of the renormalizability and unitarity of the gravitational interaction.

The aim of this Special Issue is to present a collection of original research and review articles on different approaches to quantum gravity by placing particular emphasis on the role and true meaning of higher, or even infinite, derivatives in the quantization of the gravitational interaction. Both formal aspects and applications of higher-derivative theories will be covered.

Dr. Luca Buoninfante
Prof. Dr. Gaetano Lambiase
Guest Editors

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Keywords

  • higher derivatives
  • ghosts and unitarity
  • nonlocal field theories
  • quantum gravity
  • astrophysical and cosmological applications of higher-derivative gravity

Published Papers (3 papers)

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Research

31 pages, 492 KiB  
Article
Bounce Universe with Finite-Time Singularity
by Sergei D. Odintsov and Tanmoy Paul
Universe 2022, 8(5), 292; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8050292 - 23 May 2022
Cited by 20 | Viewed by 1526
Abstract
This work explains how the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe. In particular, we examine the bounce cosmology that appears with a Type-IV singularity in the context of a ghost-free Gauss–Bonnet theory of [...] Read more.
This work explains how the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe. In particular, we examine the bounce cosmology that appears with a Type-IV singularity in the context of a ghost-free Gauss–Bonnet theory of gravity. Depending on the time of occurrence of the Type-IV singularity, three different cases may arise—when the singularity occurs before the bounce, after the bounce, or at the instant of the bounce. However, in all of these cases, we find that in the case when the singularity “globally” affects the spacetime, the scalar power spectrum becomes red-tilted, and the tensor-to-scalar ratio is too large to be consistent with the observational data. Based on these findings, we investigate a different bouncing scenario which also appears with a Type-IV singularity, and wherein the singularity affects the spacetime “locally” around the time when it occurs. As a result, and unlike the previous scenario, the perturbation modes in the second bouncing scenario are likely to be generated far away from the bounce in the deep contracting phase. This finally results in the simultaneous compatibility of the observable quantities with the Planck data and ensures the viability of the bounce model where the Type-IV singularity has local effects on the spacetime around the time of the singularity. Full article
(This article belongs to the Special Issue Higher-Derivative Theories of Gravity)
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18 pages, 869 KiB  
Article
Optical Features of AdS Black Holes in the Novel 4D Einstein-Gauss-Bonnet Gravity Coupled to Nonlinear Electrodynamics
by Khadije Jafarzade, Mahdi Kord Zangeneh and Francisco S. N. Lobo
Universe 2022, 8(3), 182; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8030182 - 14 Mar 2022
Cited by 13 | Viewed by 1501
Abstract
An alternative theory of gravity that has attracted much attention recently is the novel four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. The theory is rescaled by the Gauss-Bonnet (GB) coupling constant αα/(D4) in D dimensions and redefined [...] Read more.
An alternative theory of gravity that has attracted much attention recently is the novel four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity. The theory is rescaled by the Gauss-Bonnet (GB) coupling constant αα/(D4) in D dimensions and redefined as four-dimensional gravity in the limit D4. Thus, in this manner, the GB term yields a non-trivial contribution to the gravitational dynamics. In fact, regularized black hole solutions and applications in the novel 4D EGB gravity have also been extensively explored. In this work, motivated by recent astrophysical observations, we present an in-depth study of the optical features of AdS black holes in the novel 4D EGB gravity coupled to exponential nonlinear electrodynamics (NED), such as the shadow geometrical shape, the energy emission rate, the deflection angle and quasinormal modes. Taking into account these dynamic quantities, we investigate the effects on the black hole solution by varying the parameters of the models. More specifically, we show that the variation of the GB and NED parameters, and of the cosmological constant, imprints specific signatures on the optical features of AdS black holes in the novel 4D EGB gravity coupled to nonlinear electrodynamics, thus leading to the possibility of directly testing these black hole models by using astrophysical observations. Full article
(This article belongs to the Special Issue Higher-Derivative Theories of Gravity)
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8 pages, 252 KiB  
Communication
A Note on Singularity Avoidance in Fourth-Order Gravity
by Luca Fabbri
Universe 2022, 8(1), 51; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8010051 - 13 Jan 2022
Cited by 1 | Viewed by 1401
Abstract
We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective. Full article
(This article belongs to the Special Issue Higher-Derivative Theories of Gravity)
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