Revisiting cosmologies in teleparallelism

We discuss the most general field equations for cosmological spacetimes for theories of gravity based on non-linear extensions of the non-metricity scalar and the torsion scalar. Our approach is based on a systematic symmetry-reduction of the metric-affine geometry which underlies these theories. While for the simplest conceivable case the connection disappears from the field equations and one obtains the Friedmann equations of General Relativity, we show that in $f(\mathbb{Q})$ cosmology the connection generically modifies the metric field equations and that some of the connection components become dynamical. We show that $f(\mathbb{Q})$ cosmology contains the exact General Relativity solutions and also exact solutions which go beyond. In $f(\mathbb{T})$~cosmology, however, the connection is completely fixed and not dynamical.

Gravitational resonances on f(T)-branes

In this work, we investigate the gravitational resonances in various f(T)-brane models with the warp factor $$\text {e}^{A(y)}=\tanh \big (k(y+b)\big )-\tanh \big (k(y-b)\big )$$ e A ( y ) = tanh ( k ( y + b ) ) - tanh ( k ( y - b ) ) , where f(T) is an arbitrary function of the torsion scalar T. For three kinds of f(T), we give the solutions to the system. Besides, we consider the tensor perturbation of the vielbein and obtain the effective potentials by the Kaluza–Klein (KK) decomposition. Then we analyze what kind of effective potential can produce the gravitational resonances. The effects of different parameters on the gravitational resonances are analyzed. The lifetimes of the resonances could be long enough as regards the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates for dark matter. Combining the current experimental observations, we constrain the parameters for these brane models.

On the temporal evolution of particle production in f(T) gravity

The thermodynamical study of the universe allows particle production in modified [Formula: see text] ([Formula: see text] is the torsion scalar) theory of gravity within a flat FLRW framework for line element. The torsion scalar [Formula: see text] plays the same role as the Ricci scalar [Formula: see text] in the modified theories of gravity. We derived the [Formula: see text] gravity models by taking [Formula: see text] as the sum of [Formula: see text] and an arbitrary function of [Formula: see text] with three different arbitrary function. We observe that the particle production describes the accelerated expansion of the universe without a cosmological constant or any unknown “quintessence” component. Also, we discussed the supplementary pressure, particle number density and particle production rate for three cases.

Mesonic tilted cosmological model with wet dark fluid in F(T) theory of gravity

This study presents mesonic tilted cosmological models with wet dark fluid in the F(T) theory of gravity, which is an extension of the Teleparallel theory of gravity, where T is the torsion scalar. In this paper, a new idea is introduced about the F(T) theory of gravity with the help of tilt angle, heat conduction, and mesonic wet dark fluid. The cosmological evolution in F(T) models is investigated. The physical and geometrical aspects of the models are also discussed.

Disformal Transformations in Modified Teleparallel Gravity

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for f ( T ) gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others.

Accelerating Universe with Viscous Cosmic String in Quadratic Form of Teleparallel Gravity

In this paper, we have investigated Kantowaski-Sachs cosmological model with bulk viscous and cosmic string in the framework of Teleparallel Gravity so called f(T) gravity, where T denotes the torsion scalar. The behavior of accelerating universe is discussed towards the particular choice of f(T) = Α(T) + β(T)m. The exact solutions of the field equations are obtained by applying variable deceleration parameter which is linear in time with a negative slope. The physical behavior of these models has been discussed using some physical quantities. Also, the function of the torsion scalar for the universe is evaluated.

New traversable wormhole solutions in f(T) gravity

In this paper, we search for dynamical traversable wormhole solutions in the modified [Formula: see text] theory of gravity, [Formula: see text] being the torsion scalar. For such a wormhole, the time dependence is inserted in the static traversable wormhole metric of Morris and Thorne. Two set of tetrads are adopted: the diagonal and the nondiagonal tetrads. The diagonal set of tetrads constrains and reduces [Formula: see text] model to teleparallel theory where usual solutions have been found. With diagonal set of tetrads, free from the teleparallel theory constraint, our results show that the existence of traversable wormhole is possible only for nondynamical spacetime metric, i.e. static traversable wormhole solutions. Moreover we take into account energy condition analysis and the results show that the violation of null energy condition is not determinant for existence of static traversable wormhole solutions.

Non-minimal torsion-matter coupling and wormhole solutions

Taking into account various energy density models in the framework of torsion-based modified theory, some wormhole solutions are derived and studied. We use a non-minimal coupling between matter and torsion in order to construct the wormhole geometry for constant, exponential and Lorentzian energy density models. Two sets of torsion dependent models, including (i) teleparalell case with linear forms of torsion scalar and (ii) a [Formula: see text] gravity with quadratic form of torsion scalar, have been considered throughout this paper. Our study shows that additional terms to the Einstein field equations, due to consider modified gravity, give us the opportunity of obtaining wormhole solutions which may be supported by baryonic sources. We also check the equilibrium phase of the wormhole solutions using anisotropic and hydrostatic forces. The details of the obtained results depend on the numerical values of the free parameters that the function [Formula: see text] holds.

The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

We derive the gravitational energy–momentum pseudotensor [Formula: see text] in metric [Formula: see text] gravity and in teleparallel [Formula: see text] gravity. In the first case, [Formula: see text] is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, [Formula: see text] is the curvature-free torsion scalar derived by tetrads and Weitzenböck connection. For both classes of theories the continuity equations are obtained in presence of matter. [Formula: see text] and [Formula: see text] are non-equivalent, but differ for a quantity [Formula: see text] containing the torsion scalar [Formula: see text] and a boundary term [Formula: see text]. It is possible to obtain the field equations for [Formula: see text] and the related gravitational energy–momentum pseudotensor [Formula: see text]. Finally we show that, thanks to this further pseudotensor, it is possible to pass from [Formula: see text]–[Formula: see text] and vice versa through a simple relation between gravitational pseudotensors.

Lorentz Distributed Noncommutative F(T,TG) Wormhole Solutions

The aim of this paper is to study static spherically symmetric noncommutative F(T,TG) wormhole solutions along with Lorentzian distribution. Here, T and TG are torsion scalar and teleparallel equivalent Gauss-Bonnet term, respectively. We take a particular redshift function and two F(T,TG) models. We analyze the behavior of shape function and also examine null as well as weak energy conditions graphically. It is concluded that there exist realistic wormhole solutions for both models. We also studied the stability of these wormhole solutions through equilibrium condition and found them stable.