Torsion Scalar Research Articles

Regular solutions in f(T) -Yang-Mills theory

We consider extended covariant teleparallel $(f(T))$ gravity whose action is analytic in the torsion scalar and which is sourced by an $su(2)$ valued Yang-Mills field. Specifically, we search for regular solutions to the coupled $f(T)$ Yang-Mills system. For $f(T)=T$ we, not surprisingly, recover the Bartnik-McKinnon solitons of Einstein Yang-Mills theory. However, interesting effects are discovered with the addition of terms in the action which are nonlinear in the torsion scalar, which we specifically study up to cubic order. With the addition of the nonlinear terms the number of regular solutions becomes finite. As well, beyond critical values of the coupling constants we find that there exist \emph{no} regular solutions. These behaviors are asymmetric with respect to the sign of the nonlinear coupling constants and the elimination of regular solutions turns out to be extremely sensitive to the presence of the cubic coupling. It may be possible, therefore, that with sufficiently high powers of torsion in the action, there may be no regular Yang-Mills static solutions.

Scalar-torsion theories of gravity. II. L(T, X, Y, ϕ) theory

We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such transformations map different theories in this class onto each other.

Teleparallel gravity with scalar and vector fields

We consider a cosmological model in which a scalar field is non-minimally coupled to scalar torsion and a vector field through two coupling functions in the framework of teleparallel gravity. The explicit forms of the coupling functions and the scalar field potential are explored, under the assumption that the Lagrangian admits the Noether symmetry in the Friedmann–Lemaitre–Robertson–Walker (FLRW) space–time. The existence of such symmetry allows to solve the equations of motion and achieve exact solutions of the scale factor, scalar and vector fields. It is found that the vector field contributes significantly in the accelerating expansion of the universe in the early times, while the scalar field plays an essential role in the late times.

Phase space description of nonlocal teleparallel gravity

We study cosmological solutions in nonlocal teleparallel gravity or f(T) theory, where T is the torsion scalar in teleparallel gravity. This is a natural extension of the usual teleparallel gravity with nonlocal terms. In this work the phase space portrait proposed to describe the dynamics of an arbitrary flat, homogeneous cosmological background with a number of matter contents, both in early- and late-time epochs. The aim was to convert the system of the equations of the motion to a first order autonomous dynamical system and to find fixed points and attractors using numerical codes. For this purpose, firstly we derive effective forms of cosmological field equations describing the whole cosmic evolution history in a homogeneous and isotropic cosmological background and construct the autonomous system of the first order dynamical equations. In addition, we investigate the local stability in the dynamical systems called “the stable/unstable manifold” by introducing a specific form of the interaction between matter, dark energy, radiation and a scalar field. Furthermore, we explore the exact solutions of the cosmological equations in the case of a de Sitter spacetime. In particular, we examine the role of an auxiliary function called “gauge” eta in the formation of such cosmological solutions and show whether the de Sitter solutions can exist or not. Moreover, we study the stability issue of the de Sitter solutions both in vacuum and non-vacuum spacetimes. It is demonstrated that, for nonlocal f(T) gravity, the stable de Sitter solutions can be produced even in vacuum spacetime.

تبدیلات دوگانگی آبلی استاندارد در گرانش f(T)

According to the perturbation order, the equations of motion of low-energy string effective action are the generalized Einstein equations. Thus, by making use of the conformal transformation of the metric tensor, it is possible to map the low-energy string effective action into f(T) gravity, relating the dilaton field to the torsion scalar. Considering a homogeneous and isotropic universe and writing the canonical Lagrangian for f(T) gravity, we show that the invariance under the duality transformation holds for the cosmic scale factor a(t) at the level of the Lagrangian. Finally, by use of the dualized Lagrangian and also the invariance of torsion scalar under the scale factor duality a(t)→1/a(t), the specific form of the f(T) function is obtained.

Charged anti-de Sitter BTZ black holes in Maxwell-f(T) gravity

Inspired by the Bañados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-[Formula: see text] gravity in [Formula: see text] dimensions. The main task is to derive exact solutions for a special form of [Formula: see text], with [Formula: see text] being the torsion scalar of Weitzenböck geometry. To this end, a triad field is applied to the equations of motion of charged [Formula: see text] and sets of circularly symmetric noncharged and charged solutions have been derived. We show that, in the charged case, the monopole-like and the [Formula: see text] terms are linked by a correlative constant despite the known results in teleparallel geometry and its extensions.[Formula: see text] Furthermore, it is possible to show that the event horizon is not identical with the Cauchy horizon due to such a constant. The singularities and the horizons of these black holes are examined: they are new and have no analogue in the literature due to the fact that their curvature singularities are soft. We calculate the energy content of these solutions by using the general vector form of the energy–momentum within the framework of [Formula: see text] gravity. Finally, some thermodynamical quantities, like entropy and Hawking temperature, are derived.

Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term

Within this work, we propose a new generalised quintom dark energy model in the teleparallel alternative of general relativity theory, by considering a non-minimal coupling between the scalar fields of a quintom model with the scalar torsion component T and the boundary term B. In the teleparallel alternative of general relativity theory, the boundary term represents the divergence of the torsion vector, B=2∇μTμ, and is related to the Ricci scalar R and the torsion scalar T, by the fundamental relation: R=−T+B. We have investigated the dynamical properties of the present quintom scenario in the teleparallel alternative of general relativity theory by performing a dynamical system analysis in the case of decomposable exponential potentials. The study analysed the structure of the phase space, revealing the fundamental dynamical effects of the scalar torsion and boundary couplings in the case of a more general quintom scenario. Additionally, a numerical approach to the model is presented to analyse the cosmological evolution of the system.

Generalised nonminimally gravity-matter coupled theory

In this paper, a new generalised gravity-matter coupled theory of gravity is presented. This theory is constructed by assuming an action with an arbitrary function f(T,B,L_m) which depends on the scalar torsion T, the boundary term B=nabla _{mu }T^{mu } and the matter Lagrangian L_m. Since the function depends on B which appears in R=-T+B, it is possible to also reproduce curvature-matter coupled models such as f(R,L_m) gravity. Additionally, the full theory also contains some interesting new teleparallel gravity-matter coupled theories of gravities such as f(T,L_m) or C_1 T+ f(B,L_m). The complete dynamical system for flat FLRW cosmology is presented and for some specific cases of the function, the corresponding cosmological model is studied. When it is necessary, the connection of our theory and the dynamical system of other well-known theories is discussed.

F(T,R) theory of gravity

We mainly focus on the idea that the dynamics of the whole universe may be understood by making use of torsion [Formula: see text] and curvature [Formula: see text] at the same time. The [Formula: see text]-gravity can be considered as a fundamental gravitational theory describing the evolution of the universe. The model can produce the unification of the general relativity (GR), teleparallel gravity (TPG), [Formula: see text]-gravity and [Formula: see text]-gravity theories. For this purpose, the corresponding Lagrangian density is written in terms of an arbitrary function of the torsion and curvature scalars. Furthermore, we use the absence/existence puzzle of relativistic neutron stars and thermodynamical laws as constraining tools for the new proposal.

Induced Nonlinearities of the Scalar Field and Wormholes in the Metric-Affine Theory of Gravity

A self-gravitating scalar field with nonminimal coupling is considered in the framework of the metric-affine theory of gravity including torsion and nonmetricity. It is shown that, as a result of the interaction of this scalar fieldwith torsion and nonmetricity, a nonlinearity corresponding to the nonlinearity of the axion field can be induced, and wormholes can form.

Phase portraits of general f(T) cosmology

We use dynamical system methods to explore the general behaviour of f(T) cosmology. In contrast to the standard applications of dynamical analysis, we present a way to transform the equations into a one-dimensional autonomous system, taking advantage of the crucial property that the torsion scalar in flat FRW geometry is just a function of the Hubble function, thus the field equations include only up to first derivatives of it, and therefore in a general f(T) cosmological scenario every quantity is expressed only in terms of the Hubble function. The great advantage is that for one-dimensional systems it is easy to construct the phase space portraits, and thus extract information and explore in detail the features and possible behaviours of f(T) cosmology. We utilize the phase space portraits and we show that f(T) cosmology can describe the universe evolution in agreement with observations, namely starting from a Big Bang singularity, evolving into the subsequent thermal history and the matter domination, entering into a late-time accelerated expansion, and resulting to the de Sitter phase in the far future. Nevertheless, f(T) cosmology can present a rich class of more exotic behaviours, such as the cosmological bounce and turnaround, the phantom-divide crossing, the Big Brake and the Big Crunch, and it may exhibit various singularities, including the non-harmful ones of type II and type IV. We study the phase space of three specific viable f(T) models offering a complete picture. Moreover, we present a new model of f(T) gravity that can lead to a universe in agreement with observations, free of perturbative instabilities, and applying the Om(z) diagnostic test we confirm that it is in agreement with the combination of SNIa, BAO and CMB data at 1σ confidence level.

Lorenz gauge fixing of f(T) teleparallel cosmology

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or [Formula: see text]CDM as separate scenarios. We reconstruct the [Formula: see text] gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular [Formula: see text] gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

Noether symmetry in f(T) teleparallel gravity

Noether symmetry in teleparallel f(T) gravity, where T is the torsion scalar, has been studied in the background of Robertson–Walker space–time. It is found that Noether symmetry admits f(T)∝T32 and the associated conserved current is Σ=aa˙T12, in matter dominated era. In the process, the recent claim by Wei et al. [1] that Noether symmetry admits f(T)∝Tn, (where n is an arbitrary constant) is found not to be correct, since the conserved current satisfies the field equations only for a special choice of n=32. Further, correspondence between f(R) and f(T) theories of gravity has also been established.

New observational constraints on f(T) cosmology from radio quasars

Using a new recently compiled milliarcsecond compact radio data set of 120 intermediate-luminosity quasars in the redshift range 0.46< z <2.76, whose statistical linear sizes show negligible dependence on redshifts and intrinsic luminosity and thus represent standard rulers in cosmology, we constrain three viable and most popular f(T) gravity models, where T is the torsion scalar in teleparallel gravity. Our analysis reveals that constraining power of the quasars data (N=120) is comparable to the Union2.1 SN Ia data (N=580) for all three f(T) models. Together with other standard ruler probes such as cosmic microwave background and baryon acoustic oscillation distance measurements, the present value of the matter density parameter Omega _mathrm{m} obtained by quasars is much larger than that derived from other observations. For one of the models considered (f_1CDM) a small but noticeable deviation from Lambda CDM cosmology is present, while in the framework of f_3CDM the effective equation of state may cross the phantom divide line at lower redshifts. These results indicate that intermediate-luminosity quasars could provide an effective observational probe comparable to SN Ia at much higher redshifts, and f(T) gravity is a reasonable candidate for the modified gravity theory.

Strong magnetic field effects on neutron stars within f(T) theory of gravity

We investigate in this paper the structures of neutron stars under a strong magnetic field in the framework of f(T) gravity, where T denotes the scalar torsion. The TOV equations in this theory of gravity have been considered and the numerical resolution of these equations has been performed within the perturbative approach taking into account the equation of state of neutron dense matter in magnetic field. We simplify the problem by considering the very strong magnetic field which considerably affects the dense matter; and for quadratic and cubic corrections to the teleparallel term, one finds that the mass of neutron stars can increase for different values of the perturbation parameter. The deviation from the teleparallel term for different values of magnetic field is found out and this feature is very appreciable in the case of cubic correction. Our results are related to the hadronic particles description with very small hyperon contributions and the mass-radius evolution is consistent with the observational data.

Teleparallel conformal invariant models induced by Kaluza–Klein reduction

We study the extensions of teleparallism in the Kaluza–Klein (KK) scenario by writing the analogous form to the torsion scalar in terms of the corresponding antisymmetric tensors, given by , in the four-dimensional new general relativity (NGR) with arbitrary coefficients a, b and c. After the KK dimensional reduction, the Lagrangian in the Einstein-frame can be realized by taking 2a + b + c = 0 with the ghost-free condition for the one-parameter family of teleparallelism. We demonstrate that the pure conformal invariant gravity models can be constructed by the requirements of 2a + b = 0 and c = 0. In particular, the torsion vector can be identified as the conformal gauge field, while the conformal gauge theory can be obtained by 2a + b + 4c = 0 or 2a + b = 0, which is described on the Weyl–Cartan geometry Y4 with the ghost-free conditions 2a + b + c > 0 and . We also consider the weak field approximation and discuss the non-minimal coupled term of the scalar current and torsion vector. For the conformal invariant models with 2a + b = 0, we find that only the anti-symmetric tensor field is allowed rather than the symmetric one.

Weyl static axially symmetric field equations in modified f(T) gravity

In this paper, we obtain the field equations of Weyl static axially symmetric space-time in the framework of [Formula: see text] gravity, where [Formula: see text] is torsion scalar. We will see that, for [Formula: see text] related to teleparallel equivalent general relativity, these equations reduce to Einstein field equations. We show that if the components of energy–momentum tensor are symmetric, the scalar torsion must be either constant or only a function of radial component [Formula: see text]. The solutions of some functions [Formula: see text] in which [Formula: see text] is a function of [Formula: see text] are obtained.

Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term

We study the parameterized post-Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in Bahamonde and Wright (Phys Rev D 92:084034 arXiv:1508.06580v4 [gr-qc], 2015). We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post-Newtonian parameters. These parameters for different situations are obtained and discussed.

Interacting modified Chaplygin gas in f(T) gravity framework and analysis of its stability against gravitational perturbation

In this work, we investigate the cosmological application of modified Chaplygin gas (MCG) interacting with pressureless dark matter (DM) in the [Formula: see text] modified gravity framework, where [Formula: see text] is the torsion scalar in teleparallelism. The interaction term has been chosen proportional to the MCG density with positive coupling constant. In the Einstein general relativity (GR) framework, the interacting MCG has been found to have equation of state (EoS) parameter behaving like quintessence. However, the [Formula: see text] gravity reconstructed via the interacting MCG has been found to have EoS crossing the phantom boundary of [Formula: see text]. Thus, one can generate a quintom-like EoS from an interacting MCG model in flat universe in the modified gravity cosmology framework. The reconstructed [Formula: see text] model has been found to interpolate between dust and [Formula: see text]CDM. Stability of the reconstructed [Formula: see text] has been investigated and it has been observed that the model is stable against gravitational perturbation. Cosmological evolution of primordial perturbations has also been investigated and the self-interacting potential has been found to increase with cosmic time and the squared speed of sound has been found to be non-negative.

Analytic rotating black-hole solutions in N-dimensional f(T) gravity

A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f(T) gravity. An analytical vacuum solution is derived for the quadratic polynomial f(T)=T+epsilon T^2 and an inverse relation between the coupling constant epsilon and the cosmological constant Lambda . Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f(T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f(T) gravitational theories.