Modified Teleparallel Theories Research Articles

Exact solutions of an anisotropic universe in a modified teleparallel gravity model via the Noether and B.N.S. approaches

In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi-type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, one can not obtain a suitable solution for field equations. Hence by the use of beyond Noether symmetry (B.N.S.) approach, we solve the equations which carry Noether currents as well. By data analysis of the obtained results, compatible results with observational data at the last half of the age of universe which is accelerating are demonstrated.

The geometrical meaning of the Weitzenböck connection

In the literature, there are many discussions about the local Lorentz invariance of modified teleparallel gravity. This symmetry is obviously violated in the classical “pure tetrad” formulation of the theory, while it gets restored in the “fully covariant” approach. My claim is that, despite many heated discussions, the two formulations are just equivalent. The purpose of this note is to argue that the local Lorentz invariance is not natural for the modified teleparallel theories at all, making the pure tetrad approach more fundamentally justified.

Black holes in f(T,B) gravity: exact and perturbed solutions

Spherically symmetric solutions of theories of gravity built one fundamental class of solutions to describe compact objects like black holes and stars. Moreover, they serve as starting point for the search of more realistic axially symmetric solutions which are capable to describe rotating compact objects. Theories of gravity that do not possess spherically symmetric solutions which meet all observational constraints are easily falsified. In this article, we discuss classes of exact and perturbative spherically symmetric solutions in f(T,B)-gravity. The perturbative solutions add to the ones which have already been found in the literature, while the exact solutions are presented here for the first time. Moreover, we present general methods and strategies, like generalized Bianchi identities, to find spherically solutions in modified teleparallel theories of gravity.

General teleparallel modifications of Schwarzschild geometry

Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary function of the five possible scalars constructed from the irreducible parts of torsion. This theory is a generalization of the so-called New General Relativity theory. We find that only two scalars are different to zero in spherical symmetry and we solve the corresponding field equations analytically for conformal Teleparallel gravity, and then perturbatively around Schwarzschild geometry for the general perturbative theory around GR. Finally, we compute phenomenological effects from the perturbed solutions such as the photon sphere, perihelion shift, Shapiro delay, and the light deflection. We find their correspondent correction to the standard GR contribution and their dependence on the three model parameters.

Role of collisional matter in the framework of extended teleparallel theory

The purpose of this work is to examine the cosmic evolution in the presence of collisional matter (CM) with and without radiations in a modified Teleparallel theory involving a generic function [Formula: see text] which depends on the scalar torsion [Formula: see text] and the boundary term associated to the divergence of torsion [Formula: see text]. We select seven novel [Formula: see text] models including power law, logarithmic models and exponential models, some of these reported in [S. Bahamonde, M. Zubair and G. Abbas, Phys. Dark Univ. 19 (2018) 78; S. Bahamonde and S. Capozziello, The Eur. Phys. J. C. 77 (2017) 107; C. Escamilla-Rivera and J. L. Said, Class. Quantum Grav. 37 (2020) 165002] and discuss the evolutionary scenario. The behavior of deceleration parameter [Formula: see text], Hubble parameter [Formula: see text], Equation-of-state (EoS) for dark energy (DE) and effective EoS is presented. [Formula: see text]CDM epoch and crossing of phantom divide line (approaching to phantom era) is observed in scenarios like noncollisional matter (NCM) with radiation, CM with and without radiation. Results are found to be adequate with recent cosmic observations.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

Evolution of Collisional Matter in Modified Teleparallel Theories

Here, we discuss the cosmic evolution in the presence of collisional matter (CM) with and without radiations within the framework of modified teleparallel theories. We opt f(T, B) theory (where T stands for torsion scalar and B represents the boundary term associated to the divergence of torsion 2∇ μ Tμ = B), which makes a good connection between f(R) (R for Ricci Scalar) and f(T) (T for torsion) theory under reasonable conditions. The power law and logarithmic f(T, B) models are selected to discuss the behavior of deceleration parameter q(z), Hubble parameter H(z), Equation of state (EoS) for dark energy (DE), and effective EoS. We found the great oscillations of EoS for DE across the phantom divide line. Effective EoS also crossed the phantom divide line without any oscillations. The graphs for H(z), q(z), effective EoS are alike for NCM with radiations, CM without radiaitons and CM with radiations.

Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper, we use Noether symmetry approach for a modified teleparallel theory of gravity labeled as f ( T , B ) gravity where T is the scalar torsion and B the boundary term. Using Noether theorem, we were able to find exact spherically symmetric solutions for different forms of the function f ( T , B ) coming from Noether symmetries.

D=11 cosmologies with teleparallel structure

The presence of additional compact dimensions in cosmological models is studied in the context of modified teleparallel theories of gravity. We focus the analysis on eleven dimensional spacetimes, where the seven dimensional extra dimensions are compactified. In particular, and due to the importance that global vector fields play within the conceptual body of teleparallel modified gravity models, we consider the additional dimensions to be products of parallelizable spheres. The global vector fields characterizing the different topologies are obtained, as well as the equations of motion associated to them. Using global dynamical system techniques, we discuss some physical consequences arising because of the existence of the extra dimensions. In particular, the possibility of having an early inflationary epoch driven by the presence of extra dimensions without other matter sources is discussed.

Modified teleparallel theories of gravity in symmetric spacetimes

Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain amounts of symmetry, such as spherical or cosmological symmetry. In this article we present how to apply the notion of spacetime symmetries known from Cartan geometry to teleparallel geometries. We explicitly derive the most general tetrads and spin connections which are compatible with axial, spherical, cosmological and maximal symmetry. For homogeneous and isotropic spacetime symmetry we find that the tetrads and spin connection found by the symmetry constraints are universal solutions to the anti-symmetric part of the field equations of any teleparallel theory of gravity. In other words, for cosmological symmetry we find what has become known as "good tetrads" in the context of $f(T)$ gravity.

Can Horndeski theory be recast using teleparallel gravity?

Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second order field equations and after the GW170817 it has been severely constrained. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski gravity as a subcase and also contains many modified Teleparallel theories considered in the past, such as $f(T)$ gravity or Teleparallel Dark energy. Thus, due to the appearing of a new term in the Lagrangian, this theory can explain dark energy without a cosmological constant, may describe a crossing of the phantom barrier, explain inflation and also solve the tension for $H_0$, making it a good candidate for a correct modified theory of gravity.

Reflections on the Covariance of Modified Teleparallel Theories of Gravity

We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in f ( T ) gravity.

Energy constraints and the phenomenon of cosmic evolution in the f(T,B) framework

We investigate the cosmological evolution in a new modified teleparallel theory, called $f(T,B)$ gravity, which is formulated by connecting both $f(T)$ and $f(R)$ theories with a boundary term $B$. Here, $T$ is the torsion scalar in teleparallel gravity and $R$ is the scalar curvature. For this purpose, we assume flat Friedmann-Robertson-Walker (FRW) geometry filled with perfect fluid matter contents. We study two cases in this gravity: One is for a general function of $f(T,B)$, and the other is for a particular form of it given by the term of $-T+F(B)$. We also formulate the general energy constraints for these cases. Furthermore, we explore the validity of the bounds on the energy conditions by specifying different forms of$f(T,B)$ and $F(B)$ function obtained by the reconstruction scheme for de Sitter, power-law, the $\Lambda$CDM and Phantom cosmological models. Moreover, the possible constraints on the free model parameters are examined with the help of region graphs. In addition, we explore the evolution of the effective equation of state (EoS) $\omega_{eff}$ for the universe and compare theoretical results with the observational data. It is found that the effective EoS represents the phantom phase or the quintessence one in the accelerating universe in all of the cases consistent with the observational data.

Gravitational waves in modified teleparallel theories

We investigate the gravitational waves and their properties in various modified teleparallel theories, such as $f(T), f(T,B)$ and $f(T,T_G)$ gravities. We perform the perturbation analysis both around a Minkowski background, as well as in the case where a cosmological constant is present, and for clarity we use both the metric and tetrad language. For $f(T)$ gravity we verify the result that no further polarization modes comparing to general relativity are present at first-order perturbation level, and we show that in order to see extra modes one should look at third-order perturbations. For non-trivial $f(T,B)$ gravity, by examining the geodesic deviation equations, we show that extra polarization models, namely the longitudinal and breathing modes, do appear at first-order perturbation level, and the reason for this behavior is the fact that although the first-order perturbation does not have any effect on $T$, it does affect the boundary term $B$. Finally, for $f(T,T_G)$ gravity we show that at first-order perturbations the gravitational waves exhibit the same behavior to those of $f(T)$ gravity. Since different modified teleparallel theories exhibit different gravitational wave properties, the dvancing gravitational-wave astronomy would help to alleviate the degeneracy not only between curvature and torsional modified gravity but also between different subclasses of modified teleparallel gravities.

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.

Gravitational waves in modified teleparallel theories of gravity

Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar T, the boundary term B and a scalar field phi . The goal is to classify possible new polarizations generalizing results presented in Bamba et al. (Phys Lett B 727:194–198, arXiv:1309.2698, 2013). We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same polarization modes of General Relativity.

Effective gravitational coupling in modified teleparallel theories

In the present study, we consider an extended form of teleparallel Lagrangian $f(T,\phi,X)$, as function of a scalar field $\phi$, its kinetic term $X$ and the torsion scalar $T$. We use linear perturbations to obtain the equation of matter density perturbations on sub-Hubble scales. The gravitational coupling is modified in scalar modes with respect to the one of General Relativity, albeit vector modes decay and do not show any significant effects. We thus extend these results by involving multiple scalar field models. Further, we study conformal transformations in teleparallel gravity and we obtain the coupling as the scalar field is non-minimally coupled to both torsion and boundary terms. Finally, we propose the specific model $f(T,\phi,X)=T + \partial_\mu \phi\ \partial^\mu \phi +\xi T \phi^2$. To check its goodness, we employ the observational Hubble data, constraining the coupling constant, $\xi$, through a Monte Carlo technique based on the Metropolis-Hastings algorithm. Hence, fixing $\xi$ to its best-fit value got from our numerical analysis, we calculate the growth rate of matter perturbations and we compare our outcomes with the latest measurements and the predictions of the $\Lambda$CDM model.

New classes of modified teleparallel gravity models

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion f(Tax,Tten,Tvec), where Tax,Tten and Tvec are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or f(T) gravity. Additionally, the boundary term B which connects the Ricci scalar with the torsion scalar via R=−T+B can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or f(−T+B)=f(R) gravity, as expected.

De Sitter and scaling solutions in a higher-order modified teleparallel theory

The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equations in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of Λ-cosmology.

Generalized second law of thermodynamic in modified teleparallel theory

This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term B=2nabla _{mu }T^{mu }. This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon.