Extended Teleparallel Gravity Research Articles

Cosmological constraints on a dynamical dark energy model in F(Q) gravity

Extended teleparallel gravity, characterized by function F(Q), where Q is the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model at the present time and exhibits a special event in the future, within F(Q) gravity. To constrain the free parameters of the model, we perform Markov chain Monte Carlo (MCMC) analysis, using the last data from Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Pantheon}^{+}$$\\end{document} and the latest measurements of the H(z) parameter, combined. On the basis of this analysis, we find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime, as in the case of general relativity. Furthermore, this behavior affects the future expansion of the Universe, as it becomes decelerating at a 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} confidence level for z<-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z<-0.5$$\\end{document}, showing a bounce at zB≈-0.835\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{\ ext {B}}\\approx -0.835$$\\end{document}. We support our conclusion with a cosmographic analysis.

Exploration of GUP-corrected Casimir wormholes in extended teleparallel gravity with matter coupling

In this manuscript, we investigate the properties of Casimir wormholes within the framework of extended teleparallel gravity, incorporating the Generalized Uncertainty Principle. Both the Casimir effect and the Generalized Uncertainty Principle (GUP) originate from the concept of a fundamental minimum length. Our analysis explores the geometric and physical traits of these wormholes, examining two distinct GUP constructions namely the Kempf, Mangano, and Mann (KMM) model and the Detournay, Gabriel, and Spindel (DGS) model and their corresponding equations of state. We find that the resulting wormhole solutions exhibit anisotropic effects and violate the null energy condition, implying the presence of exotic fluid. By employing volume integral techniques, we compute the quantity of exotic fluid, providing new insights into the nature of these wormholes. Our study sheds light on the implications of GUP-corrected Casimir wormholes for our understanding of gravity and the structure of spacetime.

Constraining Extended Teleparallel Gravity via Cosmography: A Model-independent Approach

As a classical approach, the dynamics of the Universe, influenced by its dark components, are unveiled through prior modifications of Einstein’s equations. Cosmography, on the other hand, is a highly efficient tool for reconstructing any modified theory in a model-independent manner. By employing kinematic variables, it offers a profound explanation for cosmic expansion. Although the cosmographical approach has been highly successful in several geometric theories in recent years, it has not been extensively explored in coupled gravities. With this in mind, we intend to constrain an extended teleparallel gravity model, f(T,T) , through cosmographic parameters. We utilize Taylor series expansion, assuming a minimally coupled form, to constrain the unknowns involved in the series. To achieve this, we conduct a Markov Chain Monte Carlo (MCMC) analysis using three different data sets (cosmic chronometers, baryon acoustic oscillations, and Pantheon+SH0ES). The constrained results obtained from MCMC are then compared and verified using various cosmological parameters. Finally, we compare the resulting models with three well-known f(T,T) models.

Investigating novel wormhole models in extended teleparallel gravity through thin-shell composed with dark energies

This study focuses on the construction of static spherically symmetrical wormhole solutions within the framework of extended teleparallel gravity. To accomplish this, we consider the anisotropic fluid configuration satisfying the barotropic relation between the energy density and radial/tangential pressure and obtain two shape functions. For both functions, the necessary conditions to describe the existence of a wormhole geometry and the energy constraints are found to be satisfied, indicating the presence of a traversable wormhole in the vicinity of curvature-matter coupled gravity. To establish thin-shell around the wormhole geometry, we employ a cut-and-paste methodology with the Schwarzschild black hole as the outer manifold. We also explore the stability analysis of the thin-shell via linearized radial perturbations around the equilibrium shell radius for both shape functions. We study the impact of quintessence, phantom and dark energies on the dynamical configuration of thin-shell around developed wormhole structures. This study concludes that thin-shell shows maximum stability for the second choice of the shape function composed of phantom energy for massive black holes.

Structural properties of compact stars in extended Teleparallel gravity

In this study, the structures of stars are examined using the Karmarkar condition (KC) to assess the metric components. The study also takes into account the anisotropic source of the matter distribution in the context of Modified Teleparallel Rastall Gravity (MTRG). Various values of the model parameter [Formula: see text] are tested by assuming different metric coefficients for the embedding spacetime. To calculate the involved model parameters, the Schwarzschild black hole solution is employed as an exterior solution. The stability and admissibility of the solutions obtained are demonstrated by analyzing some core properties of stellar objects, using observed data from established stellar models such as “PSRJ1416-2230”. It is worth noting that the results obtained in this study are physically feasible and acceptable.

Dynamical system analysis in teleparallel gravity with boundary term

In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, f(T, B)rightarrow -T+tilde{f}(T, B), and define the dynamical variables to form the autonomous dynamical system. The critical points are obtained in two well-motivated forms of f(T, B), one that involves the logarithmic form of the boundary term B, and the other one is the non-linear form of the boundary term. The position of critical points is shown in the different evolutionary phases of the Universe such as radiation, matter, and de-Sitter phase. The stability condition of each of the critical points of both the models is derived and the behavior of each point has been obtained mathematically and through the phase portrait. The evolution of standard density parameters such as radiation (Omega _{r}), matter (Omega _{m}), and dark energy (Omega _{DE}) are also analyzed. Further to connect with the present cosmological scenario, the behavior of deceleration and equation of state parameter both in the dark energy phase (omega _{DE}) and total (omega _{tot}) are shown from the initial condition of the dynamical variables. The accelerating behaviour has been obtained for both models.

Production of primordial gravitational waves in teleparallel gravity

We study the production of primordial gravitational waves in the context of extended teleparallel gravity models and compare them with those of general relativity. Teleparallel gravity has been widely studied in the context of the late universe but not much in the early universe. Two sources of primordial gravitational waves are considered, vacuum fluctuations and tensor anisotropies within two inflation-compatible backgrounds: a perfect de Sitter and a quasi de Sitter background. We find that in the vacuum case with a perfect de Sitter background, the gravitational waves propagation equation is the same as that of general relativity, however, if the background is promoted to a quasi de Sitter background, the propagation equations are different resulting in an important difference on the tensor spectral index. When tensor anisotropies are included, we compute the most general solution for gravitational waves in terms of a retarded Green’s function and analyze the contributions to the power spectrum from these anisotropies. Finally, we investigate the energy density of these gravitational waves.

Relativistic Wormholes in Extended Teleparallel Gravity with Minimal Matter Coupling

AbstractThis study explores the wormhole solutions utilizing the notion of conformal symmetry in the background of the gravity. The exact shape functions are calculated using the Gaussian and Lorentzian distributions as the noncommutative source of the energy density. All the energy conditions are checked for the two different shape functions. The presence of exotic matter is confirmed due to the violation of the null energy conditions. The physical aspects of the epicyclic frequencies of test particles are discussed in the spacetime geometry of the obtained wormholes in the current analysis and it is shown that how they depend on the spacetime parameters. The red‐blue shifts for the photons emitted by the orbiting test particles are also investigated and their dependence on the spacetime parameters is discussed. Further, the stability of the developed structure of the traversable wormholes is investigated by using the Tolman‐Oppenheimer‐Volkoff equation.

Reconstruction of cosmological models in a general gravitational framework involving torsion scalar

This study is elaborated to reconstruct some cosmological models in the gravitational framework of an extended teleparallel gravity based on the higher-order derivative terms of torsion scalar. To achieve this goal, we consider spatially flat FRW model with perfect fluid as background matter distribution. In this framework, we find some interesting exact solutions by using the hybrid and intermediate forms of scale factor via a well-known reconstruction scheme. For exploring physical significance of the reconstructed solutions, we analyze the behavior of dark energy EoS parameter, the validity of energy condition bounds as well as the generalized second law of thermodynamics graphically. For investigating the stability of reconstructed solutions, we check the behavior of speed of sound [Formula: see text] in each case. It is seen that in de Sitter case, the reconstruction of full Lagrangian function is not possible as it reduces to the case of simple [Formula: see text] gravity which has already been discussed in literature. While for power law form of scale factor, it is found that reconstruction is possible and most of the obtained solutions favor the quintessence era of cosmic evolution. Further, it is concluded that both the energy conditions and generalized second thermodynamical law hold for the reconstructed solutions and these solutions exhibit stable behavior (as [Formula: see text]). Lastly, in case of intermediate form of scale factor, the resulting differential equations are very complicated and hence the analytical solution is possible only for the simplest case which, further, indicates cosmologically promising behavior.

Testing Born–Infeld f(T) teleparallel gravity through Sgr hbox {A}^star observations

We use observational data from the S2 star orbiting around the Galactic Center to constrain a black hole solution of extended teleparallel gravity models. Subsequently, we construct the shadow images of Sgr hbox {A}^{star } black hole. In particular, we constrain the parameter alpha =1/lambda which appears in the Born–Infeld f(T) model. In the strong gravity regime we find that the shadow radius increases with the increase of the parameter alpha . Specifically, from the S2 star observations, we find within 1sigma that the parameter must lie between 0 le alpha /M^2 le 6 times 10^{-4}. Consequently, we used the best fit parameters to model the shadow images of Sgr hbox {A}^{star } black hole and then using the Gauss-Bonnet theorem we analysed the deflection angle for leading order expansions of the parameter alpha . It is found that within the parameter range, these observables are very close to the Schwarzschild case. Furthermore, using the best fit parameters for the Born–Infeld f(T) model we show that the angular diameter is consistent with recent observations for the Sgr hbox {A}^{star } with angular diameter (51.8 pm 2.3) mu arcsec and difficult to be distinguished from the GR. For the deflection angle of light, in leading order terms, we find that the deflection angle expressed in the ADM mass coincides with the GR, but the ADM mass in the Born–Infeld f(T) gravity increases with the increase of alpha and the overall deflection angle is expected to me greater in f(T) gravity. As a consequence of this fact, we have shown that the electromagnetic intensity observed in shadow images is smaller compared to GR.

The amplification of cosmological magnetic fields in extended f(T,B) teleparallel gravity

Observations indicate that intergalactic magnetic fields have amplitudes of the order of ∼ 10-6 G and are uniform on scales of ∼ 10 kpc. Despite their wide presence in the Universe, their origin remains an open issue. Even by invoking a dynamo mechanism or a compression effect for magnetic field amplification, the existence of seed fields before galaxy formation is still problematic. General Relativity predicts an adiabatic decrease of the magnetic field evolving as |B| ∝ 1/a 2, where a is the scale factor of the Universe. It results in very small primordial fields, unless the conformal symmetry of the electromagnetic sector is broken. In this paper, we study the possibility that a natural mechanism for the amplification of primordial magnetic field can be related to extended teleparallel gravity f(T,B) models, where T is the torsion scalar, and B the boundary term. In particular, we consider a non-minimal coupling with gravity in view to break conformal symmetry in a teleparallel background, investigating, in particular, the role of boundary term B, which can be consider as a further scalar field. We find that, after solving exactly the f(T,B) field equations both in inflation and reheating eras, a non-adiabatic behavior of the magnetic field is always possible, and a strong amplification appears in the reheating epoch. We also compute the ratio r = ρB /ργ between the magnetic energy density and the cosmic microwave energy density during inflation, in order to explain the present value r ≃ 1, showing that, in the slow-roll approximation, power-law teleparallel theories with Bn have effects indistinguishable from metric theories Rn where R is the Ricci curvature scalar.

Study on anisotropic star in extended teleparallel gravity with minimal matter coupling

This manuscript explores the physical aspects of compact stars in f(τ,T) gravity, where τ and T express the torsion and trace of the energy–momentum tensor. To achieve this goal, we consider a spherically symmetric spacetime with an anisotropic source of fluid. In particular, the Karori–Barua spacetime is considered to explore the solution of compact stars. In addition, we select three specific types of compact stars models, namely PSRJ1416−2230, 4U1608−52, and CenX−3. We develop the field equations using the Karori–Barua spacetime with some specific form of f(τ,T) gravity. In addition, we consider the Schwarzschild geometry for the matching conditions at the boundary. Then, we calculate the values of all the relevant parameters by imposing matching conditions. We provide detailed graphical analyses for the physical acceptability of different parameters, namely energy density, pressure, anisotropy, and gradient. We also examine the stability of compact stars by exploring energy conditions, equations of state, conditions of causality, redshift functions, mass functions, and compactness functions. Finally, we find that the solutions we obtained are physically viable in modified physical acceptability and also it has good properties for the compact star models.

Noether symmetries and quantum cosmology in extended teleparallel gravity

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt–Deser–Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.

Cosmic acceleration and stability of cosmological models in extended teleparallel gravity

In this paper, we study the model of f(T) gravity in the presence of dark matter and modified holographic Ricci dark energy (MHRDE) in locally rotationally symmetric (LRS) Bianchi type-I space–time. To achieve a physically realistic solution of the field equations, we have considered volumetric power and exponential expansion laws. We plot the corresponding cosmological parameters for dark energy components in terms of redshift; thereafter we investigate the accelerated expansion of the Universe. The physical and geometrical parameters of the models are also discussed in detail. The Statefinder diagnostic pair and jerk parameter are analysed to characterise completely different phases of the Universe.

Focusing conditions for extended teleparallel gravity theories

In the context of extended theories of teleparallel gravity f(T) we derive the focusing conditions for a one-parameter dependent congruence of timelike auto-parallels of the Levi-Civita connection. We also consider the f(T) field equations for a general metric tensor before moving on to consider a spatially flat Robertson-Walker space-time. Following this, we study the expansion rate for a one-parameter dependent congruence of timelike auto-parallel curves of the Levi-Civita connection. Given the fact that test particles follow auto-parallels of the Levi-Civita connection, the torsion-free Raychaudhuri equation is used in order to determine the desired focusing conditions. Finally we study the obtained focusing conditions for three f(T) paradigmatic cosmological models and discuss the satisfaction or violation of these conditions. Through this, we find f(T) models that allow for the weak and strong focusing conditions to be satisfied or violated. It is mentioned that this behaviour can also be found in the so-called f(R) and f(Q) theories.

A study of anisotropic spheres in modified gravity via embedding approach

The motivation of this paper is based on the foundation of extended teleparallel gravity with matter coupling to prospect the accelerated expansion of the Universe. This theory based on the torsion scalar along with the trace term of energy stress tensor. We manipulate the spherical symmetric metric and anisotropic fluid to discuss the study of stellar structures. To interpret our research, we used the observational data of three stars. We adopt the process of parallelism of interior and exterior space-times to estimate the unspecified parameters used in the stellar discussion. Further, we discuss the stellar properties like energy density, progressive behavior of radial and tangential components of pressure, the anisotropic formation of the compact stars. We also analyze the physical presence of stars by discussing the energy conditions redshift and mass functions. We signify the stability of the system by examining the speed of sounds and EoS. We show the equilibrium of the system by analyzing the TOV equation. Finally, we show that our system in the discussion is physically stable and analytically viable.

Lorentz distributed wormhole solutions in f(T) gravity with off-diagonal tetrad under conformal motions

In this work, the possible existence of wormhole solutions have been investigated in the extended teleparallel [Formula: see text] theory of gravity by incorporating the Lorentzian source of non-commutative geometry through the conformal motion. The physical concept of conformal symmetry becomes more arguable when it is discussed in the background of non-commutative geometry, especially with the Lorentzian source. In this context, two specific different models of the extended teleparallel theory, that is, [Formula: see text], and [Formula: see text] (where [Formula: see text], [Formula: see text], [Formula: see text] being real constants and [Formula: see text] a positive integer) have been studied. The corresponding energy conditions are worked out and are analyzed graphically in the presence of the conformal motion with Lorentzian source. The presence of the exotic matter has been confirmed due to the violation of null energy conditions under some particular conditions, thereby proving the existence of the wormhole geometries in both of the models under investigation. Moreover, the stability of the wormhole geometries via the Tolman-Oppenheimer-Volkov equation has been discussed. It is concluded that these wormhole solutions supported by the non-exotic matter truly exist and are well stable under the extended teleparallel gravity.

Cosmological implications and thermodynamics of some reconstructed modified gravity models

Abstract In the context of extended teleparallel gravity theory with Gauss–Bonnet term, we reconstruct some gravitational Lagrangian functions f ( T , T G ) = T G g ( T ) and f ( T , T G ) = − T + T G g ( T ) , using some holographic dark energy models. These models include Tsallis, Renyi and Sharma–Mittal holographic dark energy models. We consider the flat FRW universe model with perfect fluid. We check the behavior of these reconstructed models through equation of state parameter for dark energy dominated era along with its plane of evolutionary parameter to check the thawing and freezing regions. In order to check the stability of the models, we explore the squared speed of sound for these models. Also, we discuss the thermodynamical analysis by checking the validity of generalized second law of thermodynamics of these reconstructed models.

Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.

Noether symmetries and boundary terms in extended Teleparallel gravity cosmology

We discuss an extended Teleparallel gravity models comprising functions of scalar invariants constructed by torsion, torsion Gauss–Bonnet and boundary terms. We adopt the Noether symmetry approach to select the functional forms, the first integrals and, eventually, the exact solutions of the dynamics in the context of flat Friedman–Robertson–Walker cosmology. Standard perfect fluid matter, minimally coupled to geometry, is considered. Several physically consistent models are derived with related exact solutions.