Realistic f(T) model describing the de Sitter epoch of the dark energy dominated universe

Abstract

We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the torsion scalar. We focus our attention on a cosmological feature of a f(T) model, checking whether it may describe the de Sitter stage of the current universe according to the evolution of the redshift, z. Our results show that the model reproduces the de Sitter stage only for low redshifts, where the perturbation function approached zero, whereas the effective parameter of the equation of state goes to -1, which is the expected behavior for any model able to reproduce the de Sitter stage. PACS Nos.: 98.80.-k, 04.50.Kd, 95.36.+x.Résumé : Nous nous penchons sur un modèle exponentiel à l'intérieur de la théorie f(T) de la gravité, où T est la torsion scalaire. Nous focalisons notre effort sur une caractéristique cosmologique du modèle f(T), vérifiant s'il peut décrire la période de de Sitter de notre univers actuel selon l'évolution du déplacement vers le rouge, z. Nos résultats montrent que le modèle reproduit la période de de Sitter seulement pour de faibles déplacements vers le rouge, là où la perturbation tend vers zéro, alors que le paramètre effectif de l'équation d'état tend vers -1, le comportement attendu de tout modèle capable de reproduire la période de de Sitter. [Traduit par la Rédaction]

Unimodular f(T) gravity

“…Our universe has experienced particular phases of evolution: after an inflationary phase it entered a phase dominated by ordinary matter and currently he lives a phase dominated by dark energy. It is known that the inflationary phase and phase dominated by dark energy can be described by a form of solution de Sitter which the scale factor is an exponential model [22,23].…”

f ( T , T ) $f(T,\mathcal{T})$ cosmological models in phase space

“…Beside several works developed within f (T, T ) [66]- [69], we can note the one undertaken by Alvarenga and collaborators [70], where they search for the model for which the covariant conservation of the energymomentum tensor is realized. In that paper they investigate the dynamics of scalar perturbations about the obtained model and focused they attention to the sub-Hubble modes and show that through the quasi-static approximation the result are very different from the ones derived in the frame of concordance ΛCDM , constraining the validity of this kind of model.…”

Geodesic Deviation Equation in ΛCDM f ( T , T ) $f(T,\mathcal {T})$ Gravity

“…By varying the action (11) with respect to the tetrads, one gets the following equations of motion [66]- [69] [∂ ξ (ee…”

“…Here, a special attention was tuned to the theory f (T, T ) as an extension of the f (T ) gravity with T the trace of energy-momentum tensor. Severals works with interessing results have been developped in this framework [66]- [69].…”