On Finslerized Absolute Parallelism Spaces

Youssef, Nabil L.; Sid-Ahmed, A. M.; Taha, Ebtsam H.

doi:10.1142/s0219887813500291

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…Recent developments attempted a global approach by using arbitrary moving frames instead of the local expressions in the natural basis [17,18]. Also, it is worth to mention other developments in teleparallel geometry: by imposing Finslerian properties to this geometrical structure [19][20][21]. Actually, this geometry provides an alternative tool for deeper studies of gravity.…”

Section: Introductionmentioning

confidence: 99%

The hidden flat like universe

Hanafy

Nashed

2015

Eur. Phys. J. C

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We study a single-fluid component in a flat like universe (FLU) governed by f (T ) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f (T ) gravity theories. Remarkably, FLU f (T ) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models k = 0, ±1. We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f (T ) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) n s the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations.

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Section: Introductionmentioning

confidence: 99%

The hidden flat like universe

Hanafy

Nashed

2015

Eur. Phys. J. C

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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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“…However, the vielbein space admits natural connections other than Weitzenböck, the later uniquely fulfills the teleparallelism condition (6). 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 $f(T)$-gravity in the absence of matter

Hanafy,

Nashed

2014

Preprint

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We derive an exact f (T ) gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (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.

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On Finslerized Absolute Parallelism Spaces

Cited by 5 publications

References 18 publications

The hidden flat like universe

The hidden flat like universe

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

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

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