Hamiltonian formulation of unimodular gravity in the teleparallel geometry

Neto, J. F. da Rocha; Maluf, J. W.; Ulhoa, S. C.

doi:10.1103/physrevd.82.124035

Cited by 30 publications

(51 citation statements)

References 26 publications

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“…There are substantial differences between their work and ours, first the fact that the Hamiltonian formulation of TEGR from which we started is different. Their work is based in a first-order formulation developed in [52][53][54], and therefore their primary and secondary constraints are different from ours, although we have almost the same number of constraints. The main difference lies in their secondary constraint π 1 = det(M ) ≈ 0, which does not appear in our formalism.…”

Section: A Discussion Of Previous Workmentioning

confidence: 98%

Hamiltonian formalism forf(T)gravity

2018

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We present the Hamiltonian formalism for f (T ) gravity, and prove that the theory has n(n−3) 2 + 1 degrees of freedom (d.o.f.) in n dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar T that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian. T is written as a quadratic form of the coefficients of anholonomy of the vierbein. We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of n(n−1) 2 primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of n(n−1) 2 − 1 first-class constraints, while one of them becomes second-class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint π ≈ 0 to remove one d.o.f. from the n 2 + 1 pairs of canonical variables. The remaining n(n−1) 2 + 2n − 1 primary constraints remove the same number of d.o.f., leaving the theory with n(n−3) 2 + 1 d.o.f. This means that f (T ) gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f.

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Section: A Discussion Of Previous Workmentioning

confidence: 98%

Hamiltonian formalism forf(T)gravity

2018

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“…which can be derived straightforwardly from the definition (261) in the case of the FRW vierbein (264). Usually, one can introduce an equation-of-state parameter w m = p m /ρ m to characterize the dynamics of the matter fluid, where the fluid satisfies the continuity equationρ…”

Section: A Equations Of Motionmentioning

confidence: 99%

“…This approach was also developed in [260,261] to investigate the constraint structure of teleparallel gravity. To begin with, we would like to slightly reformulate the Lagrangian density of f (T ) (recall that f (T ) = T + F (T ) as introduced in subsection V A) in the form of the Brans-Dick theory as follows:…”

Section: Degrees Of Freedom In F (T ) Gravitymentioning

confidence: 99%

f(T) teleparallel gravity and cosmology

et al. 2016

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Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T ) gravity, where f (T ) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T ) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T ) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T ) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T ) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T ) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to enlighten the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications. Contents

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“…It has been shown that the unimodular condition reduce the symmetry of the spacetime by one degree of freedom, since the field equations become invariant under the subgroup of the diffeomorphism, that is the transverse diffeomorphism. Therefore, the unimodular condition does not add a further constraint to reduce the degrees of freedom [49].…”

Section: A Unimodular Conditionsmentioning

confidence: 99%

Lorenz gauge fixing of f(T) teleparallel cosmology

Hanafy

Nashed

2017

Int. J. Mod. Phys. D

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In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or ΛCDM as separate scenarios. We reconstruct the f (T ) gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and standard model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular f (T ) gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.PACS numbers: 98.80.Qc, 04.20.Cv, 98.80.Cq.

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Hamiltonian formulation of unimodular gravity in the teleparallel geometry

Cited by 30 publications

References 26 publications

Hamiltonian formalism forf(T)gravity

Hamiltonian formalism forf(T)gravity

f(T) teleparallel gravity and cosmology

Lorenz gauge fixing of f(T) teleparallel cosmology

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