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14 pages, 406 KB

Open AccessArticle

First-Order Formalism and Thick Branes in Mimetic Gravity

by Qun-Ying Xie, Qi-Ming Fu, Tao-Tao Sui, Li Zhao and Yi Zhong

Symmetry 2021, 13(8), 1345; https://doi.org/10.3390/sym13081345 - 26 Jul 2021

Cited by 13 | Viewed by 2442

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations [...] Read more.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane. Full article

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18 pages, 358 KB

Open AccessArticle

Energy–Momentum Pseudotensor and Superpotential for Generally Covariant Theories of Gravity of General Form

by Roman Ilin and Sergey Paston

Universe 2020, 6(10), 173; https://doi.org/10.3390/universe6100173 - 11 Oct 2020

Cited by 3 | Viewed by 2768

Abstract

The current paper is devoted to the investigation of the general form of the energy–momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general covariance of the action without any [...] Read more.

The current paper is devoted to the investigation of the general form of the energy–momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general covariance of the action without any restrictions on the order of derivatives of the independent variables in it or their transformation laws. As a result of the generalized Noether procedure, we obtain a recurrent chain of the equations, which allows one to express canonical pEMT as a divergence of the superpotential. The explicit expression for this superpotential is also given. We discuss the structure of the obtained expressions and the conditions for the derived pEMT conservation laws to be satisfied independently (fully or partially) by the equations of motion. Deformations of the superpotential form for theories with a change in the independent variables in action are also considered. We apply these results to some interesting particular cases: general relativity and its modifications, particularly mimetic gravity and Regge–Teitelboim embedding gravity. Full article

(This article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference —International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17))

18 pages, 357 KB

Open AccessFeature PaperArticle

Non-Relativistic Limit of Embedding Gravity as General Relativity with Dark Matter

by Sergey Paston

Universe 2020, 6(10), 163; https://doi.org/10.3390/universe6100163 - 29 Sep 2020

Cited by 18 | Viewed by 2875

Abstract

Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle—our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular theory of mimetic gravity—the modification of gravity appears in [...] Read more.

Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle—our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular theory of mimetic gravity—the modification of gravity appears in both theories as a result of the change of variables in the action of General Relativity. Embedding gravity, as well as mimetic gravity, can be used in explaining the dark matter mystery since, in both cases, the modified theory can be presented as General Relativity with additional fictitious matter (embedding matter or mimetic matter). For the general case, we obtain the equations of motion of embedding matter in terms of embedding function as a set of first-order dynamical equations and constraints consistent with them. Then, we construct a non-relativistic limit of these equations, in which the motion of embedding matter turns out to be slow enough so that it can play the role of cold dark matter. The non-relativistic embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the

Λ

-Cold Dark Matter (

Λ

CDM) model. Full article

(This article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference —International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17))

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15 pages, 283 KB

Open AccessArticle

Modifications of Gravity Via Differential Transformations of Field Variables

by Anton Sheykin, Dmitry Solovyev, Vladimir Sukhanov and Sergey Paston

Symmetry 2020, 12(2), 240; https://doi.org/10.3390/sym12020240 - 5 Feb 2020

Cited by 14 | Viewed by 2635

Abstract

We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFTs) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process, the dynamics [...] Read more.

We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFTs) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process, the dynamics of the theory might either change or be conserved. After that, we concentrate on the theories of gravity which appear as a result of various DFTs applied to general relativity, namely the mimetic gravity and Regge–Teitelboim embedding theory. We review the main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFTs as the action of the original theory before DFTs plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g., for the explanation of the effects of dark matter. Full article

(This article belongs to the Special Issue Cosmology)

20 pages, 439 KB

Open AccessArticle

Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

by Marco de Cesare

Universe 2019, 5(5), 107; https://doi.org/10.3390/universe5050107 - 7 May 2019

Cited by 19 | Viewed by 4015

Abstract

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be [...] Read more.

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function f(□ϕ) implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power-law expansions of f in different regimes, corresponding e.g., to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational “constants” in the cosmological equations. Full article

(This article belongs to the Special Issue Progress in Group Field Theory and Related Quantum Gravity Formalisms)

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21 pages, 573 KB

Open AccessFeature PaperArticle

Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory

by Gamal G.L. Nashed

Symmetry 2018, 10(11), 559; https://doi.org/10.3390/sym10110559 - 1 Nov 2018

Cited by 17 | Viewed by 4441

Abstract

In this study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the [...] Read more.

In this study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the solutions derived before in general relativity theory. Using the field equations of non-linear electrodynamics mimetic theory we derive new black hole solutions with monopole and quadrupole terms. The quadruple term of those black holes is related by a constant so that its vanishing makes the solutions coincide with the linear Maxwell black holes. We study the singularities of those solutions and show that they possess stronger singularity than the ones known in general relativity. Among many things, we study the horizons as well as the heat capacity to see if the black holes derived in this study have thermodynamical stability or not. Full article

(This article belongs to the Special Issue Inflation, Universe symmetries and Modified gravity)

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18 pages, 345 KB

Open AccessFeature PaperArticle

Inflation in Mimetic f(G) Gravity

by Yi Zhong and Diego Sáez-Chillón Gómez

Symmetry 2018, 10(5), 170; https://doi.org/10.3390/sym10050170 - 17 May 2018

Cited by 42 | Viewed by 4019

Abstract

Mimetic gravity is analysed in the framework of some extensions of general relativity (GR), whereby a function of the Gauss–Bonnet invariant in four dimensions is considered. By assuming the mimetic condition, the conformal degree of freedom is isolated, and a pressureless fluid naturally [...] Read more.

Mimetic gravity is analysed in the framework of some extensions of general relativity (GR), whereby a function of the Gauss–Bonnet invariant in four dimensions is considered. By assuming the mimetic condition, the conformal degree of freedom is isolated, and a pressureless fluid naturally arises. Then, the complete set of field equations for mimetic Gauss–Bonnet gravity is established, and some inflationary models are analysed, for which the corresponding gravitational action is reconstructed. The spectral index and tensor-to-scalar ratio are obtained and compared with observational bounds from Planck and BICEP2/Keck array data. Full agreement with the above data is achieved for several versions of the mimetic Gauss–Bonnet gravity. Finally, some extensions of Gauss–Bonnet mimetic gravity are considered, and the possibility of reproducing inflation is also explored. Full article

(This article belongs to the Special Issue Symmetry: Anniversary Feature Papers 2018)

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12 pages, 935 KB

Open AccessFeature PaperConference Report

The Mimetic Born-Infeld Gravity: The Primordial Cosmos and Spherically Symmetric Solutions

by Che-Yu Chen, Mariam Bouhmadi-López and Pisin Chen

Galaxies 2017, 5(4), 87; https://doi.org/10.3390/galaxies5040087 - 27 Nov 2017

Cited by 2 | Viewed by 3451

Abstract

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions. We study a realistic primordial vacuum universe and we prove the existence of regular solutions. Besides, the linear instabilities in [...] Read more.

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions. We study a realistic primordial vacuum universe and we prove the existence of regular solutions. Besides, the linear instabilities in the EiBI model are found to be avoidable for some bouncing solutions. For a vacuum, static and spherically symmetric geometry, a new branch of solutions in which the black hole singularity that is replaced with a lightlike singularity is found. Full article

(This article belongs to the Special Issue Cosmology and the Quantum Vacuum)

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10 pages, 747 KB

Open AccessArticle

A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

by Stefano Chinaglia, Aimeric Colléaux and Sergio Zerbini

Galaxies 2017, 5(3), 51; https://doi.org/10.3390/galaxies5030051 - 7 Sep 2017

Cited by 13 | Viewed by 3740

Abstract

Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via [...] Read more.

Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied. Full article

12 pages, 270 KB

Open AccessArticle

Reissner–Nordström Anti-de Sitter Black Holes in Mimetic F(R) Gravity

by V. K. Oikonomou

Universe 2016, 2(2), 10; https://doi.org/10.3390/universe2020010 - 30 May 2016

Cited by 42 | Viewed by 5684

Abstract

In this paper, we study under which conditions the Reissner–Nordström anti-de Sitter black hole can be a solution of the vacuum mimetic

F (R)

gravity with Lagrange multiplier and mimetic scalar potential. As the author demonstrates, the resulting picture in the [...] Read more.

In this paper, we study under which conditions the Reissner–Nordström anti-de Sitter black hole can be a solution of the vacuum mimetic

F (R)

gravity with Lagrange multiplier and mimetic scalar potential. As the author demonstrates, the resulting picture in the mimetic

F (R)

gravity case is a trivial extension of the standard

F (R)

approach, and in effect, the metric perturbations in the mimetic

F (R)

gravity case, for the Reissner–Nordström anti-de Sitter black hole metric, at the first order of the perturbed variables are the same at the leading order. Full article

(This article belongs to the Collection Open Questions in Black Hole Physics)

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