scholarly journals Hamiltonian analysis of Mimetic gravity with higher derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yunlong Zheng
Keyword(s):  
Hamiltonian Formalism ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Jordan Frame ◽  
Cosmological Perturbation ◽  
Unitary Gauge ◽  
Dirac Matrix ◽  
Higher Derivatives ◽  
Mimetic Gravity ◽  
Hamiltonian Analysis

Abstract 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.

scholarly journals Hamiltonian formalism for nonlocal gravity models

2022 ◽  
Author(s):  
Pawan Joshi ◽  
Utkarsh Kumar ◽  
Sukanta Panda
Keyword(s):  
Ricci Tensor ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Lagrangian Formalism ◽  
Acceleration Of The Universe ◽  
Nonlocal Action ◽  
The Universe

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

scholarly journals Disformal Transformations in Modified Teleparallel Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 152 ◽  
Author(s):  
Alexey Golovnev ◽  
María José Guzmán
Keyword(s):  
General Relativity ◽  
Torsion Tensor ◽  
Teleparallel Gravity ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Boundary Term ◽  
Jordan Frame ◽  
Explicit Formulas ◽  
Torsion Scalar ◽  
Geometric Objects

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for f ( T ) gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others.

scholarly journals A new f(R) gravity model and properties of gravitational waves in it

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Dhruba Jyoti Gogoi ◽  
Umananda Dev Goswami
Keyword(s):  
Gravitational Waves ◽  
Gravity Model ◽  
Longitudinal Mode ◽  
Mass Scale ◽  
Gravity Models ◽  
Jordan Frame ◽  
New Model ◽  
Existing Problems ◽  
Pulsar Timing ◽  
New Directions

AbstractIn this paper, we have introduced a new f(R) gravity model as an attempt to have a model with more parametric control, so that the model can be used to explain the existing problems as well as to explore new directions in physics of gravity, by properly constraining it with recent observational data. Here basic aim is to study the properties of Gravitational Waves (GWs) in this new model. In f(R) gravity metric formalism, the model shows the existence of scalar degree of freedom as like other f(R) gravity models. Due to this reason, there is a scalar mode of polarization of GWs present in the theory. This polarization mode exists in a mixed state, of which one is transverse massless breathing mode with non-vanishing trace and the other is massive longitudinal mode. The longitudinal mode being massive, travels at speed less than the usual tensor modes found in General Relativity (GR). Moreover, for a better understanding of the model, we have studied the potential and mass of scalar graviton in both Jordan frame and Einstein frame. This model can pass the solar system tests and can explain primordial and present dark energy. Also, we have put constraints on the model. It is found that the correlation function for the third mode of polarization under certain mass scale predicted by the model agrees well with the recent data of Pulsar Timing Arrays. It seems that this new model would be useful in dealing with different existing issues in the areas of astrophysics and cosmology.

scholarly journals Classification of primary constraints for new general relativity in the premetric approach

2021 ◽  
pp. 2140003
Author(s):  
María-José Guzmán ◽  
Shymaa Khaled Ibraheem
Keyword(s):  
General Relativity ◽  
Hessian Matrix ◽  
Hamiltonian Formalism ◽  
Temporal Part ◽  
Tetrad Field ◽  
Mathematical Properties ◽  
Constitutive Tensor ◽  
Hamiltonian Analysis

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients [Formula: see text] appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients [Formula: see text]. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

scholarly journals UNAVOIDABLE CONFLICT BETWEEN MASSIVE GRAVITY MODELS AND MASSIVE TOPOLOGICAL TERMS

2004 ◽  
Vol 19 (11) ◽  
pp. 817-826 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
MARCO DIAS
Keyword(s):  
Three Dimensional ◽  
Massive Gravity ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Tree Level ◽  
Common Belief ◽  
Higher Derivative ◽  
The Common ◽  
Chern Simons ◽  
Topological Term

Massive gravity models in (2+1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz–Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern–Simons term. Furthermore, if the massive topological term is added to [Formula: see text] gravity, or to [Formula: see text] gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

scholarly journals Reconstruction of f(T) and f(R) gravity according to (m, n)-type holographic dark energy

2013 ◽  
Vol 91 (9) ◽  
pp. 703-708 ◽  
Author(s):  
M. Umar Farooq ◽  
Mubasher Jamil ◽  
Davood Momeni ◽  
Ratbay Myrzakulov
Keyword(s):  
Dark Energy ◽  
Solar System ◽  
Gravitational Constant ◽  
Holographic Dark Energy ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Torsion Scalar ◽  
Proposed Model ◽  
Gravity Theories

Motivated by earlier works (Wu and Zhu. Phys. Lett. B, 660, 293 (2008); Daouda et al. Eur. Phys. J. C, 72, 1893 (2012)), we extend them by considering a newly proposed model of (m, n)-type holographic dark energy in f(R) and f(T) gravity theories, where R and T represent Ricci scalar and torsion scalar respectively. Specifically, we reconstruct the two later gravity models and discuss their viability and cosmography. The obtained gravity models are free from ghosts, consistent with local solar system tests, and describe effective positive gravitational constant.

scholarly journals Connection dynamics of higher-dimensional scalar–tensor theories of gravity

2014 ◽  
Vol 29 (28) ◽  
pp. 1450134 ◽  
Author(s):  
Yu Han ◽  
Yongge Ma ◽  
Xiangdong Zhang
Keyword(s):  
Coupling Parameter ◽  
Hamiltonian Formalism ◽  
Symplectic Reduction ◽  
Canonical Structure ◽  
Hamiltonian Structures ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Theories Of Gravity ◽  
Two Sectors ◽  
Hamiltonian Analysis

The scalar–tensor theories (STTs) of gravity in spacetime dimensions (D+1)>2 are studied. By performing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structures in both sectors are similar to the corresponding structures of four-dimensional cases. It turns out that, similar to the case of general relativity (GR), there is also a symplectic reduction from the canonical structure of so (D+1) Yang–Mills theories coupled to the scalar field to the canonical structure of the geometrical STTs. Therefore, the non-perturbative loop quantum (LQG) gravity techniques can also be applied to the STTs in D+1 dimensions based on their connection-dynamical formalism.

scholarly journals Mimetic compact stars

2018 ◽  
Vol 15 (06) ◽  
pp. 1850091 ◽  
Author(s):  
D. Momeni ◽  
P. H. R. S. Moraes ◽  
H. Gholizade ◽  
R. Myrzakulov
Keyword(s):  
Neutron Star ◽  
Modified Gravity ◽  
Gravity Theory ◽  
Compact Stars ◽  
Gravity Models ◽  
Quark Star ◽  
Modified Gravity Models ◽  
Mimetic Gravity

Modified gravity models have been constantly proposed with the purpose of evading some standard gravity shortcomings. Recently proposed by Chamseddine and Mukhanov, the Mimetic Gravity arises as an optimistic alternative. Our purpose in this work is to derive Tolman–Oppenheimer–Volkoff equations and solutions for such a gravity theory. We solve them numerically for quark star and neutron star cases. The results are carefully discussed.

scholarly journals f(R) dual theories of quintessence: expansion-collapse duality

2021 ◽  
Vol 2021 (12) ◽  
pp. 016
Author(s):  
Dipayan Mukherjee ◽  
H.K. Jassal ◽  
Kinjalk Lochan
Keyword(s):  
Dark Energy ◽  
Cosmological Constant ◽  
Einstein Frame ◽  
Time Limit ◽  
Gravity Models ◽  
Accelerated Expansion ◽  
Jordan Frame ◽  
Late Time ◽  
Perturbative Solution ◽  
The Universe

Abstract The accelerated expansion of the universe demands presence of an exotic matter, namely the dark energy. Though the cosmological constant fits this role very well, a scalar field minimally coupled to gravity, or quintessence, can also be considered as a viable alternative for the cosmological constant. We study f(R) gravity models which can lead to an effective description of dark energy implemented by quintessence fields in Einstein gravity, using the Einstein frame-Jordan frame duality. For a family of viable quintessence models, the reconstruction of the f(R) function in the Jordan frame consists of two parts. We first obtain a perturbative solution of f(R) in the Jordan frame, applicable near the present epoch. Second, we obtain an asymptotic solution for f(R), consistent with the late time limit of the Einstein frame if the quintessence field drives the universe. We show that for certain class of viable quintessence models, the Jordan frame universe grows to a maximum finite size, after which it begins to collapse back. Thus, there is a possibility that in the late time limit where the Einstein frame universe continues to expand, the Jordan frame universe collapses. The condition for this expansion-collapse duality is then generalized to time varying equations of state models, taking into account the presence of non-relativistic matter or any other component in the Einstein frame universe. This mapping between an expanding geometry and a collapsing geometry at the field equation level may have interesting potential implications on the growth of perturbations therein at late times.

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