Although equivalent to general relativity, teleparallel gravity is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the "vector torsion". This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group $SO(1,4)$. It is found that the current state of accelerated expansion of the Universe corresponds to a late-time attractor that can be (i) a dark-energy-dominated de Sitter solution ($ω_ϕ=-1$), (ii) a quintessence-type solution with $ω_ϕ\geq-1$, or (iii) a phantom-type $ω_ϕ<-1$ dark energy.
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 [1]. 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.
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 formulate mimetic theory in f(T) teleparallel gravity where T is torsion scalar. It is shown that the construction of the mimetic theory in the teleparallel gravity requires the vierbeins to be left unchanged and the confomal transformation performed on the Minkowski metric of the tangent space. It is further argued that the conformal degree of freedom in this teleparallel mimetic theory becomes dynamical and mimics the behavior of cold dark matter. We also show that it is possible to employ the Lagrange multipliers method to formulate the mimetic theory in an f(T) theory without any auxili…
In this paper, we have investigated the physical behavior of cosmological models in the framework of modified Teleparallel gravity. This model is established using a Renyi holographic ``dark energy model (RHDE) with a Hubble cutoff. Here we have considered a homogeneous and isotropic Friedman universe filled with perfect `fluid. The physical parameters are derived for the present model in Compliances with 43 observational Hubble data sets (OHD). The equation of state (EoS) parameter in terms of $H(z)$ describes a the transition of the universe between phantom and non-phantom phases in the cont…
An important characteristic of the Dilaton cosmological model is the Gasperini-Veneziano duality transformation which follows from the existence of the $O\left( d,d\right) $ symmetry. In this study, we consider the equivalent Dilaton theory in teleparallel dark energy with the $O\left( d,d\right) $ symmetry, while the equivalent teleparallel-duality transformation is presented. The classical solution of the field equations is derived. Finally the Wheeler-DeWitt equation of quantum cosmology is discussed.
遥平行引力是广义相对论的一个等价表述，其中使用扭转标量$T$代替里奇标量$R$来表示拉格朗日密度。最近，Geng等人在（Geng et al.，2011年）。他们增加了精粹标量场，在平行引力的拉格朗日量中也允许与引力的非最小耦合，并发现这样的非最小耦合的精粹理论比广义相对论框架中的相同理论具有更丰富的结构。在扭转引力的框架下，我们对快子远程平行暗能量感兴趣，其中标量场是暗能量的来源。我们发现这种非最小耦合快子引力可以实现有效物态方程的幻影分界线的跨越。使用数值计算，我们显示这样的行为的模型明确。
The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow recently (Physics Letters B 808 (2020): 135643) in an anisotropic Bianchi type-I Universe within the framework of $% f\left( Q\right) $ symmetric teleparallel gravity, where the non-metricity scalar $Q$ is responsible for the gravitational interaction. We consider two cases: Interacting and non-interacting models of pressureless dark matter and Barrow holographic dark energy by solving $f\left( Q\right) $ symmetric teleparallel field equations. To find the exact solutions of the field…
In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe the onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via $Z_2$ symmetry breaking. While the conformal coupling holds the Universe in a state with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at the late time.
A nonminimally coupled quintessence dark energy in teleparallel model of gravity is considered. It is clarified how a matter dominated universe with initial negligible dark energy density can evolve to a late time de Sitter space-time via the $Z_2$ symmetry breaking.
Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second order field equations and after the GW170817 it has been severely constrained. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski grav…
In this work, we have discussed a spatially homogeneous and anisotropic Bianchi type-I space-time in the presence of Barrow holographic dark energy (infrared cut-off is the Hubble's horizon) proposed by Barrow recently (Physics Letters B 808 (2020): 135643) and matter in the framework of $f(Q)$ gravity where the non-metricity $Q$ is responsible for the gravitational interaction for the specific choice of $f(Q)=λQ^{2}$ (where $λ<0$ is a constant). To find the exact solutions to the field equations we consider the deceleration parameter $q$ is a function of the Hubble's parameter $H$ i.e. $q=b-\…
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…
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, $B=2\nabla_μT^μ$, 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 qui…
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 explore an extension of the symmetric teleparallel gravity denoted the $f(Q)$ theory, by considering a function of the nonmetricity invariant $Q$ as the gravitational Lagrangian. Some interesting properties could be found in the $f(Q)$ theory by comparing with the $f(R)$ and $f(T)$ theories. The field equations are derived in the $f(Q)$ theory. The cosmological application is investigated. In this theory the accelerating expansion is an intrinsic property of the universe geometry without need of either exotic dark energy or extra fields. And the state equation of the geometrical dark energy…
The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the Friedmann-Robertson-Walker (FRW) line element. The energy of the universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the …
We study the growth rate of matter perturbations in the context of teleparallel dark energy in a flat universe. We investigate the dynamics of different theoretical scenarios based on specific forms of the scalar field potential. Allowing for non-minimal coupling between torsion scalar and scalar field, we perform a phase-space analysis of the autonomous systems of equations through the study of critical points. We thus analyze the stability of the critical points, and discuss the cosmological implications searching for possible attractor solutions at late times. Furthermore, combing the growt…
Statefinder diagnostic is a convenient method that can differentiate between the various dark energy models. In this article, we analyze the statefinder parameters in symmetric teleparallel cosmology. The $f(Q)$ gravity theory is an alternative theory to GR, where gravitational interactions attribute to the non-metricity scalar $Q$. In the present work, we consider two $f(Q)$ models which contains a linear and a non-linear form of non-metricity scalar, specifically, $f(Q)=αQ + \fracβ{Q}$ and $f(Q)=αQ + βQ^2$, where $α$ and $β$ are free parameters and then statefinder parameters $(r,s)$ are eva…
A quantum cosmology in teleparallel gravity is presented in this article. Teleparallel gravity is used to perform such an analysis once in General Relativity (GR) the concept of gravitational energy is misleading preventing the establishment of a concise quantum cosmology. The Wheeler-DeWitt like equation is obtained using the Weyl quantization and the teleparallel expression of energy.
