Embedding theory as new geometrical mimetic gravity

Paston, S. A.; Sheykin, A. A.

doi:10.1140/epjc/s10052-018-6474-9

Cited by 31 publications

(65 citation statements)

References 33 publications

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“…The metric here is assumed to be an independent variable, and the condition (1) appears as a consequence of the equations of motion. In Reference [36], several ways to choose S add were considered. Let us introduce two of them which seem the most promising in the context of the analysis of embedding matter properties.…”

Section: Embedding Gravitymentioning

confidence: 99%

“…so the independent quantity τ µν , which is playing the role of a Lagrange multiplier, turns out to be an EMT of embedding matter. As an alternative, one can assume the independence of the set of currents j µ a in Equation (6) instead of τ µν (y a is still independent) [36]:…”

Section: Embedding Gravitymentioning

confidence: 99%

“…In this framework, one can try to explain the effects of DM in the assumption of a strict spatial homogeneity and isotropy of the universe [33,35]. To do it at the smaller scales, one might try to reformulate the theory as the GR with an additional contribution corresponding to some fictitious matter [36] and to examine the properties of this embedding matter. The number of variables that describe embedding matter turns out to be sufficiently large, and the properties of this matter are sufficiently rich to hope for a successful description of observational properties of DM in the framework of embedding gravity, without the introduction of additional extensions (as it is done, e.g., in the framework of mimetic gravity).…”

Section: Introductionmentioning

confidence: 99%

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

Paston

2020

Universe

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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 (ΛCDM) model.

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Section: Embedding Gravitymentioning

confidence: 99%

Section: Embedding Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Paston

2020

Universe

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“…Note that j, β and λ differ from used in Ref. [11] by a multiplier like √ −g. Note that due to (4) the motion of mimetic matter in the original formulation is governed by only one scalar function λ, so one has to extend this formulation to allow more general motion.…”

Section: Regge-teitelboim Embedding Theorymentioning

confidence: 99%

“…where g ind is the determinant of the induced metric (11). The application of the above procedure gives…”

Section: Branementioning

confidence: 99%

Polyakov-like approach to the modified gravity and other geometric theories

Sheykin

Ioffe

Manida

et al. 2020

Int. J. Geom. Methods Mod. Phys.

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We study the procedure that allows to rewrite the actions of some modified gravity theories like mimetic gravity and Regge-Teitelboim embedding theory as Einstein-Hilbert actions with additional matter contributions. It turns out that this procedure can be applied to brane action, which lead to a polynomial brane action. We also examine the connection between this procedure and Polyakov trick in string theory.

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Hamiltonian analysis of Mimetic gravity with higher derivatives

Zheng

2021

J. High Energ. Phys.

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Two types of mimetic gravity models with higher derivatives of the mimetic field are analyzed in the Hamiltonian formalism. For the first type of mimetic gravity, the Ricci scalar only couples to the mimetic field and we demonstrate the number of degrees of freedom (DOFs) is three. Then in both Einstein frame and Jordan frame, we perform the Hamiltonian analysis for the extended mimetic gravity with higher derivatives directly coupled to the Ricci scalar. We show that different from previous studies working at the cosmological perturbation level, where only three propagating DOFs show up, this generalized mimetic model, in general, has four DOFs. To understand this discrepancy, we consider the unitary gauge and find out that the number of DOFs reduces to three. We conclude that the reason why this system looks peculiar is that the Dirac matrix of all secondary constraints becomes singular in the unitary gauge, resulting in extra secondary constraints and thus reducing the number of DOFs. Furthermore, we give a simple example of a dynamic system to illustrate how gauge choice can affect the number of secondary constraints as well as the DOFs when the rank of the Dirac matrix is gauge dependent.

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Embedding theory as new geometrical mimetic gravity

Cited by 31 publications

References 33 publications

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

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

Polyakov-like approach to the modified gravity and other geometric theories

Hamiltonian analysis of Mimetic gravity with higher derivatives

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