This thesis investigates the characteristics of modified teleparallel gravity models that incorporate a scalar field and a trace of the energy-momentum tensor, with particular attention to their cosmological effects, especially regarding late-time cosmic acceleration. Teleparallel gravity, as an alternative framework to General Relativity, defines gravity through torsion rather than curvature, and when combined with a scalar field, it allows exploration of a wider variety of cosmological scenarios. This thesis examines the late-time acceleration of the Universe and its various phases through dynamical system analysis within the framework of modified teleparallel gravity theories. It presents the mathematical formulations of $f(T)$, $f(T, \mathcal{T})$, $f(T, ϕ)$, Horndeski teleparallel gravity, and the quintessence dark energy model, along with the application of dynamical systems and relevant cosmological datasets. Overall, the results demonstrate that these modified teleparallel gravity models provide viable descriptions of the late-time cosmic acceleration and offer insights into the dynamics of the Universe beyond standard cosmology.
The work is devoted to LRS Bianchi I domain walls cosmological models within the framework of teleparallel gravity using volumetric expansions laws for the depiction model. The physical and kinematical properties are discussed. The statefinder parameters are also analysed along with the jerk parameter and cosmological constraints.
We describe the fully gauge invariant cosmological perturbation equations in braneworld teleparallel gravity. In this theory, perturbations are the result of small fluctuations in the pentad field. We derive the gauge invariant 'potentials' for both geometric and matter variables. Unlike the metric fluctuations in general relativity, pentad perturbations can only contain scalar and vector modes. As a result, in teleparallel gravity, tensor modes including gravitational waves, come from the contortion tensor.
This paper has been removed by arXiv administrators because it plagiarizes gr-qc/0303034, "The energy of the universe in teleparallel gravity," by T. Vargas; and Gen relativ. Grav. 37(6) 1151-1152 (2005), "The taub solution again," by Robert T. Jantzen.
Teleparallel gravity offers a path to resolve a number of longstanding issues in general relativity by re-interpreting gravitation as an artifact of torsion rather than curvature. The present work deals with cosmological solutions in an extension of teleparallel gravity. A reconstruction scheme of the theory has been proposed based on the cosmological jerk parameter. The work contains analysis of ensuing cosmological parameters for different viable models and the stability of the models against cosmic time through an investigation of perturbation of matter overdensity and the hubble parameter.
In the present paper we discuss dynamic of anisotropic Bianchi I Universe filled by the perfect fluid in teleparallel $f(T)$-gravity. By using as analytical as numerical approaches we confirm the main results of previous authors such as presence of future isotropic attractor and find a number of the new one such as existence of essential number of bounce solutions and possibility to construct late time acceleration without any specific matter.
In this paper we have investigated some rip cosmological models in an extended symmetric teleparallel gravity theory. We consider the form $f(Q,T)=aQ^m+bT$ in the Einstein-Hilbert action and expressed the field equations and the dynamical parameters in terms of the non-metricity $Q$. Three rip models such as Little Rip, Big Rip and Pseudo Rip are presented. The energy conditions and the cosmographic parameters are derived and analysed for all these models.
We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gr…
Scalar-tensor theories offer the prospect of explaining the cosmological evolution of the Universe through an effective description of dark energy as a quantity with a non-trivial evolution. In this work, we investigate this feature of scalar-tensor theories in the teleparallel gravity context. Teleparallel gravity is a novel description of geometric gravity as a torsional-rather than curvature-based quantity which presents a new foundational base for gravity. Our investigation is centered on the impact of a nontrivial input from the kinetic term of the scalar field. We consider a number of mo…
We investigate the Universe evolution at late-time stages in models of teleparallel gravity with power-law nonminimal coupling and a decreasing power-law potential of the scalar field $ϕ$. New asymptotic solutions are found analytically for these models in vacuum and with a perfect fluid. Applying numerical integration, we show that the cosmological evolution leads to these solutions for some region of the initial conditions, and these asymptotic regimes are stable with respect to homogeneous variations of the initial data. The physical sense of the results is discussed.
We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space-time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild-de Sitter solution of Einstein's equation, and then to the Robertson-Walker Universe. We show that in the first case our method leads to an average energy density of the vacuum space-time, and in latter case the energy vanishes in the case o…
A detailed dynamical analysis of the tachyonic teleparallel dark energy model, in which a non-canonical scalar field (tachyon field) is non-minimally coupled to gravitation, is performed. It is found that, when the non-minimal coupling is ruled by a dynamically changing coefficient $α\equiv f_{,ϕ}/\sqrt{f}$, with $f(ϕ)$ an arbitrary function of the scalar field $ϕ$, the universe may experience a field-matter-dominated era "$ϕ$MDE", in which it has some portions of the energy density of $ϕ$ in the matter dominated era. This is the most significant difference in relation to the so-called telepar…
In this study, cosmological models with perfect fluid and a gravitational framework f(Q) will be examined. In this modified theory of gravity, the gravitational force has the form f(Q), where Q stands for the non-metricity scalar. I create two bouncing cosmological models, one in which the Lagrangian f(Q) is assumed to have a linear dependence on Q and the other in which it has a polynomial functional form. It has been discovered that the parameters of the individual models largely determine how they will behave. The resulting models' equation of state (EoS) parameter captures the universe's i…
Well-tempering is a promising classical method of dynamically screening an arbitrarily large vacuum energy and generating a late-time, low energy de Sitter vacuum state. In this paper, we study for the first time self-tuning in teleparallel gravity and obtain well-tempered cosmological models in the teleparallel gravity analogue of Horndeski theory. This broadens the scope of well-tempered cosmology and teases the potentially far richer cosmological dynamics that could be anchored on teleperallel gravity. We expand the well-tempered recipe to its most general form so far and use it to search f…
Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of telepara…
In the framework of teleparallel gravity, the Friedman-Robertson-Walker cosmological model with scalar tensor theory where scalar field is non-minimally coupled to both the torsion scalar and boundary term is studied. Utilizing the Noether symmetry approach in such a theory, we obtain the explicit forms of the couplings and potential as a function the scalar field. We present some important cosmological solutions for the modified field equations using these functions getting via the Noether symmetry approach. Finally, the interesting cosmological properties of these solutions are discussed in …
We study the conservation laws in the teleparallel theory with a positive cosmological constant, an extension of the teleparallel theory possessing solutions with de Sitter asymptotics. Demanding that the canonical generators of the asymptotic symmetry are well defined, we obtain their improved form, which defines the conserved charges of the theory. The physical interpretation of the results is discussed.
In this work, we study a cosmological model of Bianchi type-I Universe in teleparallel gravity for a perfect fluid. To obtain the cosmological solution of the model, we assume that the deceleration parameter is a linear function of the Hubble parameter $H$ i.e. $q=-1+βH$ (where $β$ as a positive constant). Consequently, we get a model of our Universe, where it goes from the initial phase of deceleration to the current phase of acceleration. We have discussed some physical and geometric properties such as Hubble parameter, deceleration parameter, energy density, pressure, and equation of state …
Considering the vacuum as characterized by the presence of only the gravitational field, we show that the vacuum energy density of the de Sitter space, in the realm of the teleparallel equivalent of general relativity, can acquire arbitrarily high values. This feature is expected to hold in the consideration of realistic cosmological models, and may possibly provide a simple explanation to the cosmological constant problem.
To recreate the cosmological models, we employed the parametrization approach in modified teleparallel Gauss-Bonnet gravity. It has been interesting to apply the parametrization approach to investigate cosmological models. The real benefit of using this method is that the observational data may be incorporated to examine the cosmological models. Several cosmological parameters were examined, such as the Hubble parameter (H), the deceleration parameter (q), and the equation of state (EoS) parameter (w). The results obtained are consistent with recent cosmological findings in the conventional sc…
In the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lemaître-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without…
Cosmological perturbations are considered in $f(T)$ and in scalar-torsion $f(φ)T$ teleparallel models of gravity. Full sets of linear perturbation equations are accurately derived and analysed at the relevant limits. Interesting features of generalisations to other teleparallel models, spatially curved backgrounds, and rotated tetrads are pointed out.
Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld…
We discuss linear perturbations of the most general class of teleparallel spacetimes with cosmological symmetry, and perform a decomposition of these perturbations into irreducible components. We then study their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms of the background spacetime, and derive a full set of gauge-invariant perturbation variables. Comparing our results with perturbations around the diagonal tetrad corresponding to a spatially flat teleparallel background cosmology, we see the appearance of new terms which depend on the particular choice of a cosm…
In this paper, we investigate the existence of bulk viscous FLRW cosmological models in a recently proposed extended symmetric teleparallel gravity or $f\left( Q,T\right) $ gravity in which $Q$ is the non-metricity and $T$ is the trace of the energy-momentum tensor. We consider a simple coupling between matter and non-metricity, specifically, $f\left( Q,T\right) =αQ^{m+1}+λT$ and $f\left( Q,T\right) =αQ+λT$ where $α$, $λ$ and $m$ are free model parameters. The exact cosmological solutions are found by assuming the scale factor in the form of the hybrid expansion law. This type of relation gene…
The existence of self-similar solutions is discussed in symmetric teleparallel $f(Q)$-theory for a Friedmann-Lemaître-Robertson-Walker background geometry with zero and non-zero spatial curvature. For the four distinct families of connections which describe the specific cosmology in symmetric teleparallel gravity, the functional form of $f(Q)$ is reconstructed. Finally, to see if the analogy with General Relativity holds, we discuss the relation of the self-similar solutions with the asymptotic behaviour of more general $f(Q)$ functions.
The stationary cosmological model without closed timelike curves of Gödel type is obtained for the ideal dust matter source within the framework of the teleparallel gravity. For a specific choice of the teleparallel gravity parameters, this solution reproduces the causality violating stationary Gödel solution in general relativity, in accordance with the teleparallel equivalent of general relativity. The relation between the axial-vector torsion and the cosmic vorticity is clarified.
Scalar-Tensor Symmetric Teleparallel Gravity: Reconstruct the Cosmological History with a Steep Potential
Universiti Tunku Abdul Rahman（苏丹依德里斯教育大学）；Universiti Malaya（马来亚大学）；Universidad Catòlica del Norte（北天主教大学）；Durban University of Technology（德班理工大学）；North-West University（西北大学）
We study teleparallel gravitational theories with are invariant under the conformal transformations. Wide family of the gravitational Lagrangians that are invariant under conformal transformations have investigated. Cosmological solutions inspired by the observational data for a flat Universe in the vacuum has been found. To add matter fields to the cosmological models by preserving the conformal symmetry there are significant limitations. Friedmann-Robertson-Walker (FRW) equations based on the effective terms of energy density and pressure have been rewriting and continuity equation for the e…
Symmetric Teleparallel Gravity is an exceptional theory of gravity that is consistent with the vanishing affine connection. This theory is an alternative and a simpler geometrical formulation of general relativity, where the non-metricity $Q$ drives the gravitational interaction. Our interest lies in exploring the cosmological bouncing scenarios in a flat Friedmann-Limaître-Robertson-Walker (FLRW) spacetime within this framework. We explore bouncing scenarios with two different Lagrangian forms of $f(Q)$ such as a linearly and non-linearly dependence on $Q$. We have successfully examined all t…
In the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lemaître-Robertson-Walker geometry. We shall study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, the matter bounce and singular bounce. Some of the Lagrangians discovered are both analytical at the origin having Minkowski and Schwarzsc…
We apply the teleparallelism condition to the Poincaré gauge theory of gravity. The resultant teleparallelized cosmology is completely equivalent to the Friedmann cosmology derived from Einstein's general theory of relativity. The torsion is shown to play the role of the cosmological constant driving the cosmic acceleration. We then extend such theory to include the effect of spin and explore the possibility of accounting for the current accelerating universe by a spinning dark energy.
We consider the teleparallel equivalent of Lovelock gravity and its natural extension, where the action is given by an arbitrary function $f(T_{_{L_1}}, T_{_{L_2}},\cdot \cdot \cdot , T_{_{L_n}})$ of the torsion invariants $T_{_{L_i}}$, which contain higher order torsion terms, and derive its field equations. Then, we consider the special case of $f(T_{_{L_1}}, T_{_{L_2}})$ gravity and study a cosmological scenario by selecting a particular $f(T_{_{L_1}}, T_{_{L_2}})$, and derive the Friedmann equations. Also, we perform a dynamical systems analysis to extract information on the evolution of t…
Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity
School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Department of Physics, New Uzbekistan University（新乌兹别克斯坦大学物理系）；Center for Astronomy and Astrophysics, Center for Field Theory and Particle Physics and Department of Physics, Fudan University（复旦大学天文与天体物理中心、场论与粒子物理中心及物理系）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Space Sciences and Astronomy, University of Malta（马耳他大学空间科学与天文研究所）；Department of Physics, University of Malta（马耳他大学物理系）
We consider the notion of cosmological symmetry, i.e., spatial homogeneity and isotropy, in the field of teleparallel gravity and geometry, and provide a complete classification of all homogeneous and isotropic teleparallel geometries. We explicitly construct these geometries by independently employing three different methods, and prove that all of them lead to the same class of geometries. Further, we derive their properties, such as the torsion tensor and its irreducible decomposition, as well as the transformation behavior under change of the time coordinate, and derive the most general cos…
In this paper, we have examined the recently proposed modified symmetric teleparallel gravity, in which gravitational Lagrangian is given by an arbitrary function of non-metricity scalar $Q$. We have considered a constant jerk parameter to express the Hubble rate. Moreover, we have used 31 points of OHD datasets and 1701 points of Pantheon+ datasets to constraint our model parameters by means of the Markov Chain Monte Carlo analysis. The mean values and the best fit obtained give a consistent Hubble rate and deceleration parameter compared to the observation values. In order to study the curre…
This paper explores the possibility of treating the exotic Chaplygin-gas (CG) fluid model as some manifestation of an $f(T)$ gravitation. To this end, we use the different cosmological CG equations of state, compare them with the equation of state for the modified teleparallel gravity and reconstruct the corresponding Lagrangian densities. We then explicitly derive the equation of state parameter of the torsion fluid $w_T$ and study its evolution for vacuum-torsion, radiation-torsion, dust-torsion, stiff fluid torsion, and radiation-dust-torsion multi-fluid systems. The obtained Lagrangians ha…
The parity violating gravity models based on the symmetric teleparallel gravity have been considered in the literature, but their applications in cosmology and especially the modifications to cosmological perturbations have not been fully explored. In this paper we consider such a simple model which modifies general relativity by a parity non-conserved coupling, within the framework of the symmetric teleparallel gravity. We study in detail its cosmological applications and focus on its cosmological perturbation theory. Besides the already known parity violation in the tensor perturbations, we …
Different models of universes are considered in the context of teleparallel theories. Assuming that the universe is filled by a fluid with equation of state (EoS) $P=-ρ-f(ρ)$, for different teleparallel theories and different EoS we study its dynamics. Two particular cases are studied in detail: in the first one we consider a function $f$ with two zeros (two de Sitter solutions) that mimics a huge cosmological constant at early times and a pressureless fluid at late times. In the second one, in the context of loop quantum cosmology with a small cosmological constant, we consider a pressureless…
Teleparallel Horndeski theory offers an avenue through which to circumvent the speed constraint of gravitational waves in an efficient manner. However, this provides an even larger plethora of models due to the increase in action terms. In this work we explore these models in the context of cosmological systems. Using Noether point symmetries, we classify the dynamical systems that emerge from Teleparallel Horndeski cosmologies. This approach is very effective at selecting specific models in the general class of second-order Teleparallel scalar-tensor theories, as well as for deriving exact so…
Even though it is not possible to differentiate General Relativity from Teleparallel Gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of General Relativity, and similar effects are also expected to occur in Teleparallel Gravity. Here, we study nonlocal deformations of Teleparallel Gravity along with its cosmological solutions. We observe that Nonlocal Teleparallel Gravity (like nonlocal General Relativity) is consistent with the present cosmological dat…
In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here …
We consider three-dimensional gravity based on torsion. Specifically, we consider an extension of the so-called Teleparallel Equivalent of General Relativity in the presence of a scalar field with a self-interacting potential, where the scalar field is non-minimally coupled with the torsion scalar. Then, we find asymptotically AdS hairy black hole solutions, which are characterized by a scalar field with a power-law behavior, being regular outside the event horizon and null at spatial infinity and by a self-interacting potential, which tends to an effective cosmological constant at spatial inf…
In this paper we use the conformal teleparallel gravity to study an isotropic and homogeneous Universe which is settled by the FRW metric. We solve the field equations and we obtain the behavior of some cosmological parameters such as scale factor, deceleration parameter and the energy density of the perfect fluid which is the matter field of our model. The field equations, that we called modified Friedmann equations, allow us to define a dark fluid, with dark energy density and dark pressure, responsible for the acceleration in the Universe.
We investigate exact and analytic solutions for the field equations in teleparallel dark energy model where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exist for the description of the field equations and variational symmetries are applied for the construction of invariant functions and conservation laws. The later are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantu…
We consider curvature-teleparallel $F(R,T)$ gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar $R$ and the torsion scalar $T$. Using the Noether Symmetry Approach, we show that the functional form of the $F(R, T)$ function, can be determined by the presence of symmetries . Furthermore, we obtain exact solutions through to the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.
In this paper, working in a Friedman-Lemaitre-Robertson-Walker (FLRW), first, in the flat case, we recover the generalized Friedman equation of Quantum Loop cosmology, and therefore the cosmological bounce, in the framework of modified teleparallel gravity $f(T)$-model, $T$ being the torsion scalar introduced in teleparallel gravity approach, without invoking unconventional exotic matter. Furthermore we study the associated perturbations again in a flat FLRW space-time. Then, we generalize the results to the curved FLRW space-time, where some issues related to the choice of tetrad exist, by us…
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are mostly not equivalent to the traditional route to modified gravity. $f(T,B)$ gravity is one such gravitational theory where the second and fourth order contributions to the field equations are decoupled. In this work, we explore the all important cosmological perturbations of this new framework of gravity. We derive the gravitational propagation equation, its vec…
