Narrow Results

In this paper, we first obtain the energy density by the approach of the new agegraphic dark energy model, and then the $f(T,B)$ gravity model is studied as an alternative to the dark energy in a viscous fluid by flat-FRW background, in which $T$ and $B$ are torsion scalar and boundary term. The Friedmann equations will be obtained in the framework of modified teleparallel gravity by tetrad components. We consider that the universe dominates with components such as matter and dark energy by an interacting model. The Hubble parameter is parameterized by the power-law for the scale factor, and then we fit the corresponding Hubble parameter with observational data constraints. The variation of the equation of state (EoS) for dark energy is plotted as a function of the redshift parameter, and the accelerated expansion of the universe is explored. In what follows, the stability of the model is also studied on the base of the sound speed parameter. Finally, the generalized second law of thermodynamics is investigated by entropies of inside and on the boundary of the apparent horizon in thermodynamics equilibrium.

In this paper, we have explored the field equations of $f(T,B)$ gravity and determined the dynamical parameters with the hyperbolic function of Hubble parameter. The accelerating behavior has been observed and the behavior of equation of state parameter indicates the $\mathrm{\Lambda }$CDM model at late time. The role of model parameters in assessing the accelerating behavior has been emphasized. Interestingly, the term containing $\beta$, the coefficient of boundary term, in the model parameter vanishes during the simplification. The scalar perturbation has been presented to show the stability of the model.

In this paper, we investigate the conformal vector fields (CVFs) of static cylindrically symmetric (SCS) spacetimes in $f(T,B)$ gravity, a novel modified teleparallel gravity that connects both $f(T)$ and $f(R)$ theories via a boundary term $B$. Initially, we employ an algebraic approach to extract some classes that represent SCS solutions in $f(T,B)$ gravity. Applying the above-mentioned approach, we find solutions in nine cases. We also investigate the CVFs using the direct integration technique. Following a thorough investigation, we discover that the spacetimes admit proper CVFs in only one case. In rest of the eight cases, the spacetimes either become conformally flat or they admit homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the spacetimes under consideration has come out to be 5, 6 or 15. To complete the study, we also compute the energy density and pressure of each model. Corresponding to the resulting models, we discuss the energy conditions in order to check the physical sound of the solutions.

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 $f(T,B)$ which depends on the scalar torsion $T$ and the boundary term associated to the divergence of torsion $2{\nabla }_{\mu }{T}^{\mu }=B$. We select seven novel $f(T,B)$ 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 $q(z)$, Hubble parameter $H(z)$, Equation-of-state (EoS) for dark energy (DE) and effective EoS is presented. $\mathrm{\Lambda }$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.

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the $f(T,B)$ 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 $f(T,B)$ 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.

The aim of this paper is to classify locally rotationally symmetric (LRS) Bianchi type I space-times via conformal vector fields (CVFs) in the $f(T,B)$ gravity. In a first step, we find the space-times that are solutions of some $f(T,B)$ gravity model. Furthermore, we classify the resulting space-times via CVFs. During the classification, there arise eight cases. Reviewing each case thoroughly, we find that in two cases, the space-times confess proper CVFs. The space-times in rest of the six cases either become conformally flat or tends to admit homothetic vector fields (HVFs) or the Killing vector fields (KVFs).

In this paper, we have explored the field equations of $f(T,B)$ gravity as an extension of teleparallel gravity in an isotropic and homogeneous space-time. In the basic formalism developed, the dynamical parameters are derived by incorporating the power law and exponential scale factor function. The models show accelerating behavior and approach $\mathrm{\Lambda }$CDM at late time. The present value of the equation of state parameter for both the cases is obtained to be in accordance with the range provided by cosmological observations. The geometrical parameters and the scalar field reconstruction are performed to assess the viability of a late-time accelerating universe. Further, the stability of both the models is presented. It has been observed that both the models are parameter-dependent. Since most of the geometrically modified theories of gravity favor the violation of strong energy condition (SEC), we have derived the energy conditions both for the power law and exponential model. In both the models, the violation of SEC is established.