Linear connections and curvature tensors in the geometry of parallelizable manifolds

Youssef, Nabil L.; Sid-Ahmed, A. M.

doi:10.1016/s0034-4877(07)00020-1

Cited by 42 publications

(45 citation statements)

References 10 publications

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“…The AP-condition (3) together with the above noncommutation formula force the curvature tensor R α µνσ of the canonical connection Γ α µν to vanish identically [21]. Moreover, the parallelization vector fields define a metric tensor on M by…”

Section: A Teleparallel Spacementioning

confidence: 99%

The hidden flat like universe II

Hanafy

Nashed

2016

Astrophys Space Sci

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In a recent work, a particular class of f (T ) gravity, where T is the teleparallel torsion scalar, has been derived. This class has been identified by flat-like universe (FLU) assumptions [1]. The model is consistent with the early cosmic inflation epoch. A quintessence potential has been constructed from the FLU f (T )-gravity. We show that the first order potential of the induced quintessence is a quasi inverse power law inflation with an additional constant providing an end of the inflation with no need to an extra mechanism. At e-folds N * = 55 before the end of the inflation, this type of potential can perform both E and B modes of the cosmic microwave background (CMB) polarization pattern.

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Section: A Teleparallel Spacementioning

confidence: 99%

The hidden flat like universe II

Hanafy

Nashed

2016

Astrophys Space Sci

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“…It is worth to see different approaches to study gravity by examining connections other than Weitzenböck [51][52][53][54][55][56][57][58], which may have an interesting astrophysical and cosmological applications [59][60][61][62]. One can show that equation (6) implies the metricity condition.…”

Section: A Installing Weitzenböck Connectionmentioning

confidence: 99%

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

Hanafy¹,

Nashed²

2016

Astrophys Space Sci

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We derive an exact f (T ) gravity in the absence of ordinary matter in Friedmann-RobertsonWalker (FRW) universe, where T is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor T µν of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential (inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained f (T ) acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the f (T ) contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field (tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the f (T ) theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential.PACS numbers: 98.80.Qc, 04.20.Cv, 98.80.Cq.

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“…[48], [50], [51] and [52]). Since the tensor gµν is a covariant second order symmetric tensor and the matrix (gµν) is non-degenerate, then gµν can be used to play the role of the metric of a Riemannian space associated with the AP-space.…”

Section: A Brief Review Of Ap-geometrymentioning

confidence: 99%

“…Afterwards, it is shown that this tensor is neither curvature nor torsion, it is a geometric alloy made of the two tensors and cannot be defined except in the AP-space. So it has been given the name W-tensor [50]. It has been used in constructing the Generalized Field Theory (GFT) using the dual connection (Γ α µν ).…”

Section: Skew-symmetric Tensors Symmetric Tensorsmentioning

confidence: 99%

Unification Principle and a Geometric Field Theory

2015

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Abstract:In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

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Linear connections and curvature tensors in the geometry of parallelizable manifolds

Cited by 42 publications

References 10 publications

The hidden flat like universe II

The hidden flat like universe II

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

Unification Principle and a Geometric Field Theory

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