Torsion Scalar Research Articles

Observational Constraints and Cosmographic Analysis of f(T,TG) Gravity and Cosmology

We perform observational confrontation and cosmographic analysis of f(T,TG) gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss–Bonnet combination, and gives rise to an effective dark-energy sector which depends on the extra torsion contributions. We employ observational data from the Hubble function and supernova Type Ia Pantheon datasets, applying a Markov chain Monte Carlo sampling technique, and we provide the iso-likelihood contours, as well as the best-fit values for the parameters of the power-law model, an ansatz which is expected to be a good approximation of most realistic deviations from general relativity. Additionally, we reconstruct the effective dark-energy equation-of-state parameter, which exhibits a quintessence-like behavior, while in the future the Universe enters into the phantom regime, before it tends asymptotically to the cosmological constant value. Furthermore, we perform a detailed cosmographic analysis, examining the deceleration, jerk, snap, and lerk parameters, showing that the transition to acceleration occurs in the redshift range 0.52≤ztr≤0.89, as well as the preference of the scenario for quintessence-like behavior. Finally, we apply the Om diagnostic analysis to cross-verify the behavior of the obtained model.

Exploration of bulk viscous Bianchi type cosmological model in f(T) theory of gravity

In the present paper, the expansion of Locally Rotational Symmetric (LRS) Bianchi type - I cosmological model have been investigated with Bulk Viscous matter in the context of f(T) theory of gravity, where T signifies the torsion scalar. The power model, exponential model and linear functional model of the universe have been discussed for choices of f(T)with utilization of the special form of time dependent varying deceleration parameter. The discussion involves the examination of the dynamical behaviour of these models using some dynamical parameters and its graphical representation.

Late times ΛCDM f(T) gravity model with parameterized q(z)

According to a number of astronomical studies, the universe is currently undergoing an accelerated expansion phase. We employed the recently proposed gravity, which holds that the current accelerated expansion phase of the universe is caused by a torsion scalar. The investigation is carried out using a parameterization of [Formula: see text] (where [Formula: see text] and [Formula: see text] are the model parameters) and the [Formula: see text] using [Formula: see text] is obtained. The model shows good agreement with recent observations, such as the LCDM model at late times. Finally, we examined how the cosmological parameters behaved in for constrained values.

Accelerating universe in f(T) teleparallel gravity

In recent decades, there has been significant research on the role of torsion in gravity, with a focus on aligning gravity with its gauge formulation and including spin into a geometric description. In order to account for the present phenomenon of the universe’s accelerated expansion, recent developments have introduced [Formula: see text] theories that rely on the disparities found in teleparallel gravity. Torsion, rather than curvature, is the fundamental geometric property that describes gravity in these theories. When compared to theories involving [Formula: see text] functions, the field equations are consistently of second order and surprisingly simple. We consider a specific type of function called torsion, which is defined as [Formula: see text]. The expression consists of two free parameters, [Formula: see text] and [Formula: see text], and the current value of the torsion scalar, [Formula: see text]. In order to solve the modified torsion field equations (MTFEs), we can utilize the parametrization of the deceleration parameter (DP) in terms of redshift, denoted as [Formula: see text]. Here, [Formula: see text] and [Formula: see text] represent the model parameters. The model parameters are determined by utilizing observable constraints, including as 57 Hubble data points, 1048 Pantheon supernovae type Ia data, and Baryon Acoustic Oscillations (BAO) datasets. In addition, we utilize Markov Chain Monte Carlo (MCMC) methods for statistical analysis.

Energy exchange between charged relativistic fluids in f(T) gravity

This study focuses on the effects of a polytropic fluid on a charged gravitational source within f(T) gravity, where T is the torsion scalar. We investigate how the electromagnetic field affects the flow of energy in spherically symmetric and static celestial objects that contain relativistic fluids. By using the gravitational decoupling technique, we analyze the effects of polytropic fluid on the dynamics of the gravitational source, accompanied by the matching of the interior geometry with an exterior at the hypersurface Σ. Finally, with the help of the Tolman IV solution, we observe the conduct of energy conditions with the existence of charge using f(T) field equations and got the intended outcomes.

Effect of torsion and electric charge parameters on the configuration of anisotropic compact stars in [formula omitted] gravity

Under the assumption of a linear f(T) function, we present a new exact solution for an anisotropic and charged stars in the background of f(T)-gravity. By considering ansatz for the metric potential, charge function, and anisotropy function, we have arrived at an exact and nonsingular solution to the field problem. The anisotropy and charge function are discovered to be contingent upon the existence of the torsion scalar, and the evolution of the charge and anisotropy of the stellar matter is significantly influenced by variations in the torsion parameter ζ1. The features of anisotropy and charged compact star at the boundary are examined by making the interior metric solution correspond to the exterior Reissner-Nordström-de Sitter solution. The physical validity of the derived quantities is shown graphically, and the energy conditions are found to be satisfied. The causality condition, hydrostatic stable equilibrium, and adiabatic stability are also verified for the chosen values of the torsion parameter. The M−R relations are analyzed for the charged and anisotropic stellar configurations in f(T)-gravity. It is found that increasing values of the torsion parameter ζ1 enhance the maximum mass of the star while increasing values of the charge parameter q0 decrease the maximum mass. The influence of anisotropy via increasing the torsion parameter could be a probable interpretation of the maximum masses exceeding 2.5 M⊙, as observed in the case of the secondary companion of GW190814. Interestingly, our study sheds light on the characteristic of non-singular solutions to the field equations in f(T)-gravity with linear f(T).

Stellar modeling with quintessence field via embedding approach in Ratsall teleparallel gravity

This paper proposes a new model for anisotropic compact stars with quintessence in Rastall teleparallel gravity via embedding approach. In the gravity, the acquired field equations encompassing the anisotropic matter source as well as the quintessence field are studied using the specific character of the scalar torsion [Formula: see text] for the observed stars candidates PSRJ[Formula: see text]1416–2230, 4U[Formula: see text]1608–52, CenX–3, EXO 1785–248 and SMC[Formula: see text]X–1. All of the stellar structures under consideration are said to be advantageously independent of any central singularity and are stable. A thorough graphical analysis reveals that numerous physical properties critical for forming stellar structures are satisfied.

Neutron stars in scalar torsion theories with non minimal coupling

We explore the existence and configurations of static and slowly rotating neutron stars (NSs) within a specific truncation of teleparallel scalar torsion theory. In this model, a scalar field ϕ is non-minimally coupled to the torsion scalar as ξTϕ 2, in the presence of the scalar potential V(ϕ) = -μ 2 ϕ 2/2 + λϕ 4/4. We establish the hydrostatic equilibrium equations for the static scenario and numerically solve them for both interior and exterior regions, employing appropriate boundary conditions near the center and at a distant location far away from the star's surface. Radial profiles of metric functions and the scalar field, alongside mass-radius diagrams, are plotted, utilizing four different realistic equations of state (EOS). Our results align closely with observational constraints from the GW170817 event, revealing a maximal mass of 2.37 M ⊙ achieved with the BSk21 EOS for a coupling parameter ξ = 0.25. Extending our analysis to encompass slow rotation, we establish the relationship between the star's moment of inertia and its mass. Furthermore, we explore future observations of NSs utilizing the redshift surface observable. Finally, we demonstrate the validity of the universality relation between the two forms of normalized moment of inertia within teleparallel scalar torsion theory with non minimal coupling.

Perfect Fluid with Heat Flow in f(T) Theory of Gravity

Bianchi Type-I cosmological models have been a subject of extensive research in cosmology due to their simplicity and relevance in understanding the dynamics of the early Universe. In this study, we investigate the dynamics of such models within the framework of f(T) gravity, an alternative theory of gravity that extends teleparallel gravity by introducing a general function of the torsion scalar, T. We focus on the presence of a perfect fluid with heat flow in the cosmic medium. By solving the field equations of f(T) gravity, we obtain exact solutions for the Bianchi Type-I cosmological models. These solutions provide valuable insights into the evolution of the Universe and how it is influenced by the modified gravity theory. Furthermore, we derive cosmological parameters in terms of redshift, offering a convenient way to interpret observational data and connect theoretical predictions to empirical measurements. Our findings not only contribute to a deeper understanding of the dynamics of Bianchi Type-I cosmological models but also provide a foundation for comparing f(T) gravity with standard general relativity in the context of observational cosmology. This research paves the way for further exploration of alternative gravity theories and their implications for the early Universe’s evolution and structure.

Dynamical system analysis in multiscalar-torsion cosmology

We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann–Lemaître–Robertson–Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields’ kinetic and potential components. We employ exponential functions for the scalar field potentials and analyse the field equations’ equilibrium points to reconstruct the cosmological evolution. Remarkably, we discover many equilibrium points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and late time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe.

Scalar-multi-tensor approach to fT,B,∇μT,∇μB teleparallel gravity

In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type fT,B,∇μT,∇μB , where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.

Compact stars in f(T)=T+ξTβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T) = T +\\xi T^\\beta $$\\end{document} gravity

The Teleparallel Theory is equivalent to General Relativity, but whereas in the latter gravity has to do with curvature, in the former gravity is described by torsion. As is well known, there is in the literature a host of alternative theories of gravity, among them the so called extended theories, in which additional terms are added to the action, such as for example in the f(R) and f(T) gravities, where R is the Ricci scalar and T is the scalar torsion, respectively. One of the ways to probe alternative gravity is via compact objects. In fact, there is in the literature a series of papers on compact objects in f(R) and f(T) gravity. In particular, there are several papers that consider f(T)=T+ξT2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T) = T + \\xi T^2$$\\end{document}, where ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} is a real constant. In this paper, we generalise such extension considering compact stars in f(T)=T+ξTβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f (T ) = T + \\xi T^\\beta $$\\end{document} gravity, where ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} are real constants and looking out for the implications in their maximum masses and compactness in comparison to the General Relativity. Also, we are led to constrain the β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} parameter to positive integers which is a restriction not imposed by cosmology.

Phase transition of Bianchi-type I cosmological model in [formula omitted] gravity

In the context of the f(T) theory of gravity, where T represents as a torsion scalar, we explore the Locally Rotational Symmetric Bianchi type-I dark energy model. An effective cosmological model is used, and its isotropization is examined, producing a conclusion that accurately depicts the evolution of our Universe. We looked at dark energy (DE) and dark matter (DM) in both interacting and non-interacting forms. The exact solution of the field equations was achieved by using special form of the time-varying deceleration parameter in terms of the Hubble parameter. The dark matter energy density (Ω(dm)) decreases with redshift while dark energy density (Ω(de)) grow with redshift. The physical and geometrical behaviour of the models are examined in both forms. A combination of dark matter and dark energy can eliminate the coincidence issue in the ΛCDM model. Using the most recent observations, we also discussed the physical characteristics of the generated models about the early Universe and late-time acceleration. It has been noted that this model has an initial singularity, initial decelerating growth and late-time transitions to an accelerating expansion phase.

Reconstruction of [formula omitted] Lagrangian for various cosmological scenarios

In this paper we explore a reconstruction scheme in the background of the f(T,T) gravity theory for different cosmological scenarios, where T is the scalar torsion and T is the trace of the energy-momentum tensor. Using the reconstruction technique f(T,T) Lagrangian is constructed for different cosmological eras such as dust, ΛCDM, perfect fluid, etc. Both minimal and non-minimal matter coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed f(T,T) functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late time accelerated expansion of the universe.

A description of classical and quantum cosmology for a single scalar field torsion gravity

In the background of homogeneous and isotropic flat FLRW spacetime, both classical and quantum cosmologies have been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field have been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extent so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler–DeWitt (WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the WD equation becomes solvable. Finally, quantum description shows finite nonzero probability at the classical big bang singularity.

Conformal Fisher information metric with torsion

We consider torsion in parameter manifolds that arises via conformal transformations of the Fisher information metric, and define it for information geometry of a wide class of physical systems. The torsion can be used to differentiate between probability distribution functions that otherwise have the same scalar curvature and hence define similar geometries. In the context of thermodynamic geometry, our construction gives rise to a new scalar—the torsion scalar defined on the manifold, while retaining known physical features related to other scalar quantities. We analyse this in the context of the Van der Waals and the Curie–Weiss models. In both cases, the torsion scalar has non trivial behaviour on the spinodal curve. We also briefly comment on the one dimensional classical Ising model and show that the torsion scalar diverges exponentially near criticality.

Conformal motions of anisotropic exact Bianchi type II models admitting energy conditions in f(T) gravity

The purpose of this paper is to explore the anisotropic exact Bianchi type II solutions in [Formula: see text] gravity, where [Formula: see text] denotes the torsion scalar. We utilize the solutions to discuss conformal vector fields (CVFs) and energy conditions. In the first slot of this study, we find the CVFs. The CVFs being a generalization of the Killing vector fields (KVFs) are affiliated with the conservation laws of physics. Corresponding to the obtained solutions, we observe law of conservation of (linear or generalized) momentum. In the second slot, we derive the constraints under which the solution classes can admit certain energy conditions.

Cosmology of a Chaplygin Gas Model Under f(T) Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas (GCG) with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences, studied in terms of equation of state (EoS) parameter. In the non-interacting scenario, the EoS parameter behaves as quintessence in both forms of the scale factor. In the interacting scenario, the EoS parameter behaves as phantom and for the truncated form of the scale factor, it violates the constraints of the positive parameter α. The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T) modified gravity, where T is the torsion scalar in teleparallelism. The interaction term is directly proportional to the GCG density with positive coupling constant. In f(T) gravity, the EoS is behaving like phantom. The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations, i.e., the squared speed of sound is non-negative and an increasing function of cosmic time t. We have observed that our reconstructed f(T) model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis. Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

Constraining [formula omitted] gravity with gravitational baryogenesis

Gravitational baryogenesis is one of the mechanisms which help us to explore more about our early universe, especially baryon-anti-baryon asymmetry. As we know, modified theories of gravity are very successful in describing the present accelerated scenario of the universe. Therefore, in this letter, we aim to constrain the generalized torsion-based modified theory of gravity, namely, f(T,T) gravity with gravitational baryogenesis, where T, T are the torsion scalar, trace of the energy-momentum tensor, respectively. For this, we examine how the various Lagrangian forms of f(T,T) affect the baryogenesis. We also impose the constraints on the extra degrees of freedom induced by modified theory with the observational values of the baryon-to-entropy ratio. In addition, we further explore how more generalized gravitational baryogenesis can attribute in a physically viable and consistent way to the cosmologies of the modified theory of gravity.

Mass of compact stars in f(T) gravity

The mass of compact objects in General Relativity (GR), which as is well known, is obtained via the Tolman–Oppenheimer–Volkov (TOV) equations, is a well defined quantity. However, in alternative gravity, this is not in general the case. In the particular case of f(T) gravity, where T is the scalar torsion, some authors consider that this is still an open question, since it is not guaranteed that the same equation used in TOV GR holds. In this paper we consider such an important issue and compare different ways to calculate the mass of compact objects in f(T) gravity. In particular, we argue that one of them, the asymptotic mass, may be the most appropriate way to calculate mass in this theory. We adopt realistic equations of state in all the models presented in this article.