f(T)f(T) gravity and energy distribution in Landau-Lifshitz prescription

We investigate in this paper the Landau-Lifshitz energy distribution in the framework of $f(T)$ theory view as a modified version of Teleparallel theory. From some important Teleparallel theory results on the localization of energy, our investigations generalize the Landau-Lifshitz prescription from the computation of the energy-momentum complex to the framework of $f (T)$ gravity as it is done in the modified versions of General Relativity. We compute the energy density in the first step for three plane symmetric metrics in vacuum. We find for the second metric that the energy density vanishes independently of $f (T)$ models. These metrics provide results in perfect agreement with those mentioned in literature. In the second step the calculations are performed for the Cosmic String Spacetime metric. It results that the energy distribution depends on the mass $M$ of cosmic string and it is strongly affected by the parameter of the considered $f (T)$ quadratic model.Comment: 23 pages, 4 figure

Holographic dark energy model in unimodular f(T)f(T) gravity

The present work deals with holographic dark energy in the context of unimodular $f(T)$ gravity, which is a modification of teleparallel gravity. We develop the general reconstruction procedure of the $f(T)$ form that can yield the holographic feature of the dark energy. We fit the reconstructed model with the $H(z)$ data and our results show a perfect agreement with the WMAP9 cosmological observational data, at least for the range $-1.10\leq \omega_V \leq -1.05$. We investigate the consistency of the reconstructed model by studying its stability against linear gravitational and matter perturbations, fixing $\omega_V$ to $-1.05$. The model presents stability for both de Sitter and power-law solutions and we conclude that it is a good candidate as alternative viable model for characterizing holographic dark energy.Comment: 13 pages and 4 figure

Stability and Space Phase Analysis in f(R) theory with Generalized Exponential model

We have studied in this paper, the stability of dynamical system in $f(R)$ gravity. We have considered the $f(R)$ $\gamma$-gravity and explored its dynamical analysis. We found six critical points among which only one describes an universe fulled of both matter and dominated dark energy. It's shown that these critical points presents specific phase spaces described by the corresponding fluids. Furthermore, we've investigated the stability conditions of these critical points and find that theses conditions are dependent of the model parameters. We also study the stability of a new power-law $f_\ast(R)$ model with de Sitter and power law solutions.Comment: 16 pages and 6 figures, version accepted for publication in IJMP

Unimodular f(T) gravity

We reconstruct the geometrical $f(T)$ actions in the framework of unimodular $f(T)$ gravity. The unimodular $f(T)$ gravity yields stunning properties related to the generalized Friedmann equations. Indeed, it has been found that depending on the form of the Friedmann equations, the Lagrange multipliers may or not depend on the time parameter $\tau$. Moreover we find that the reconstruction of $f(T)$ functions can be easily performed in general, not depending on a given scale factor, or can determine a particular way, depending on a given scale factor, in the vacuum. It is noted that the reconstruction of a general action joins is consistent to the unimodular gravity for the constant $\Lambda$Comment: 11 page

Geodesic Deviation Equation in Λ\LambdaCDM f(T,T)f(T,\mathcal{T}) gravity

The geodesic deviation equation has been investigated in the framework of $f(T,\mathcal{T})$ gravity, where $T$ denotes the torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor, respectively. The FRW metric is assumed and the geodesic deviation equation has been established following the General Relativity approach in the first hand and secondly, by a direct method using the modified Friedmann equations. Via fundamental observers and null vector fields with FRW background, we have generalized the Raychaudhuri equation and the Mattig relation in $f(T,\mathcal{T})$ gravity. Furthermore, we have numerically solved the geodesic deviation equation for null vector fields by considering a particular form of $f(T,\mathcal{T})$ which induces interesting results susceptible to be tested with observational data.Comment: 20 pages, 2 figure

f(T,T)f(T,\mathcal{T}) Cosmological Models in Phase Space

In this paper we explore $f(T, \mathcal{T})$, where $T$ and $\mathcal{T}$ denote the torsion scalar and the trace of the energy-momentum tensor respectively. We impose the covariant conservation to the energy-momentum tensor and obtain a cosmological $f(T, \mathcal{T})$ respectively. We impose the covariant conservation to the energy-momentum tensor and obtain a cosmological $f(T, \mathcal{T})$ model. Then, we study the stability of the obtained model for power-law and de Sitter solutions and our result show that the model can be stable for some values of the input parameters, for both power-law and de Sitter solutions.Comment: 23 pages, 16 figure

Scalar perturbations and conformal transformation

The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedmann-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other formalisms

Inflationary scenario driven by type IV singularity in f(T)f(T) gravity

In this paper, we investigate the effects of Type IV singularity through $f(T)$ gravity description of inflationary universe, where $T$ denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a $f(T)$ model according to a given Hubble rate susceptible to describe the inflationary era near the type IV singularity. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV Singularity, indicating that a dynamical instability of the cosmological system occurs a that point. This means that the dynamical cosmological evolution up to that point, ceases to be the final attractor since the system is abruptly interrupted. Furthermore, by considering the $f(T)$ trace anomaly equation and the slow-roll conditions, we deal with the de Sitter inflationary description of the reconstructed model. As results, the model leads to a conditional instability, view as the source of the graceful exit from inflation. Our theoretical $f(T)$ description based on slow-roll parameters not only confirms some observational data on spectral index and the scalar-to-tensor ratio from Planck data and BICEP$2$/Keck-Array data, but also shows the property of $f(T)$ gravity in describing the early and late-time evolution of our universe.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1510.04333, arXiv:1511.07586 by other author

Locally Rotationally Symmetric Bianchi Type-I cosmological model in f(T)f(T) gravity: from early to Dark Energy dominated universe

We study the locally rotational symmetry Bianchi type-I dark energy model in the framework of $f(T)$ theory of gravity, where $T$ denotes the torsion scalar. A viable cosmological model is undertaken and the isotropization of this latter is checked, yielding a result that reflects the real evolution of our universe. Moreover, still in the anisotropic optic, a more complicated $f(T)$ model is obtained from the cosmological reconstruction scheme and the analysis shows that the universe is more anisotropic at the beginning if the terms of higher order in $T$ are not considered. This means that the non-linear model should be favoured by observational data.Comment: 20 pages, 10 figures, Accepted for publication in International Journal of Modern Physics D (IJMPD

Charged Black Holes in Generalized Teleparallel Gravity

In this paper we investigate charged static black holes in 4D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f(T) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f(T) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.Comment: 16 pages, 3 figure, version accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP