scholarly journals Modifications of Gravity Via Differential Transformations of Field Variables

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 240 ◽  
Author(s):  
Anton Sheykin ◽  
Dmitry Solovyev ◽  
Vladimir Sukhanov ◽  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Lagrange Multipliers ◽  
Additional Term ◽  
Field Theories ◽  
Original Theory ◽  
Embedding Theory ◽  
Differential Field ◽  
Theories Of Gravity ◽  
Mimetic Gravity

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.

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

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 173
Author(s):  
Roman Ilin ◽  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Wide Class ◽  
Equations Of Motion ◽  
General Covariance ◽  
Independent Variables ◽  
Theories Of Gravity ◽  
Generally Covariant ◽  
Derivatives Of ◽  
Mimetic Gravity

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.

Field Equation of Nonlocal Gravity

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Gravitational Field ◽  
Field Equation ◽  
Abelian Group ◽  
Gravitational Field Equation ◽  
Differential Field ◽  
Einstein's Equation ◽  
Future Theory ◽  
World Function

In extended general relativity (GR), Einstein’s field equation of GR can be expressed in terms of torsion and this leads to the teleparallel equivalent of GR, namely, GR||, which turns out to be the gauge theory of the Abelian group of spacetime translations. The structure of this theory resembles Maxwell’s electrodynamics. We use this analogy and the world function to develop a nonlocal GR|| via the introduction of a causal scalar constitutive kernel. It is possible to express the nonlocal gravitational field equation as modified Einstein’s equation. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. The field equation of NLG can be expressed as Einstein’s field equation with an extra source that has the interpretation of the effective dark matter. It is possible that the kernel of NLG, which is largely undetermined, could be derived from a more general future theory.

scholarly journals Erratum: Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity [Phys. Rev. D92, 064045 (2015)]

2016 ◽  
Vol 93 (10) ◽  
Author(s):  
Emmanuele Battista ◽  
Simone Dell’Agnello ◽  
Giampiero Esposito ◽  
Luciano Di Fiore ◽  
Jules Simo ◽  
...  
Keyword(s):  
General Relativity ◽  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Test Bed ◽  
Lagrangian Points ◽  
Theories Of Gravity

scholarly journals RECONSTRUCTING f(R, T) GRAVITY FROM HOLOGRAPHIC DARK ENERGY

2012 ◽  
Vol 21 (03) ◽  
pp. 1250024 ◽  
Author(s):  
M. J. S. HOUNDJO ◽  
OLIVER F. PIATTELLA
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Energy Momentum Tensor ◽  
Holographic Dark Energy ◽  
Momentum Tensor ◽  
Ricci Scalar ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Theories Of Gravity

We consider cosmological scenarios based on f(R, T) theories of gravity (R is the Ricci scalar and T is the trace of the energy–momentum tensor) and numerically reconstruct the function f(R, T) which is able to reproduce the same expansion history generated, in the standard General Relativity theory, by dark matter and holographic dark energy. We consider two special f(R, T) models: in the first instance, we investigate the modification R + 2f(T), i.e. the usual Einstein–Hilbert term plus a f(T) correction. In the second instance, we consider a f(R) + λT theory, i.e. a T correction to the renown f(R) theory of gravity.

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

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 163 ◽  
Author(s):  
Sergey Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Cold Dark Matter ◽  
Equations Of Motion ◽  
Dynamical Equations ◽  
Relativistic Limit ◽  
Change Of Variables ◽  
Modified Theory ◽  
Mimetic Gravity

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.

scholarly journals Earth-moon Lagrangian points as a test bed for general relativity and effective field theories of gravity

2015 ◽  
Vol 92 (6) ◽  
Author(s):  
Emmanuele Battista ◽  
Simone Dell’Agnello ◽  
Giampiero Esposito ◽  
Luciano Di Fiore ◽  
Jules Simo ◽  
...  
Keyword(s):  
General Relativity ◽  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Test Bed ◽  
Lagrangian Points ◽  
Theories Of Gravity

Beyond the Standard Model

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Supergravity Models ◽  
Standard Model ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Super Symmetry ◽  
The Standard Model ◽  
Topological Field ◽  
Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

scholarly journals Modeling dark matter halos with nonlinear field theories

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
R. A. C. Correa ◽  
P. H. R. S. Moraes ◽  
A. de Souza Dutra ◽  
O. L. Dors ◽  
W. de Paula ◽  
...  
Keyword(s):  
Dark Matter ◽  
Field Theories ◽  
Dark Matter Halos ◽  
Nonlinear Field

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

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