Rafael Ferraro
Gauge symmetries in teleparallel gravity, together with the identities among the dynamical equations they provide, are analyzed in relation to the way they condition the coupling between matter and gravity. Particularly, the coupling of fermionic matter seems to be excluded in a wide range of teleparallel theories.
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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.
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.
We consider the cosmology derived from $f(T,B)$ gravity where $T$ is the torsion scalar and $B=\frac{2}{e}\partial_μ(e T^μ)$ a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel $f(T)$ gravity, the curvature $f(R)$ gravity and the teleparallel-curvature $f(R,T)$ gravity, which are particular cases of $f(T,B)$. We adopt the Noether Symmetry Approach to study the related dynamical systems and to find out cosmological solutions.
The Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity
本文提出一个基于Noether方法的统一形式体系，用于在TEGR和STEGR中构造守恒量，引入“规范”概念并讨论其选择对守恒量的影响。
A generalized teleparallel cosmological model, $f(T_\mathcal{G},T)$, containing the torsion scalar $T$ and the teleparallel counterpart of the Gauss-Bonnet topological invariant $T_{\mathcal{G}}$, is studied in the framework of the Noether Symmetry Approach. As $f(\mathcal{G}, R)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet topological invariant and $R$ is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, $f(T_\mathcal{G},T)$ contains all the possible information directly related to the torsion tensor. In th…
Hao Wei et.al. has claimed in $\mathrm{Phys. Lett. \textbf{B707}, 298 (2012)}$ that Noether symmetry in the context of teleparallel $f(T)$ theory of gravity admits $f(T)\propto T^{n}$, (where $n$ is an arbitrary) in matter domain era in Friedmann- Robertson universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general. Here, it is shown that Noether Symmetry admits $f(T)\propto T^\frac{3}{2}$ along with a conserved current $ a \dot a T^\frac{1}{2}$ in teleparallel $f(T)$ gravity. Thus, their claim is not correct.
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.
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 …
The Noether charge associated to diffeomorphism invariance in teleparallel gravity is derived. It is shown that the latter yields the ADM mass of an asymptotically flat spacetime. The black hole entropy is then investigated based on Wald's prescription that relies on the Noether charge. It is shown that, like in general relativity, the surface gravity can be factored out from such a charge. Consequently, the similarity with the first law of thermodynamics implied by such an approach in general relativity does show up also in teleparallel gravity. It is found that, based on the expression of th…
In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, we can not obtain a suitable solution for field equations. Hence by the use of B.N.S. approach, we solve the equations which carry Noether currents as well. By data an…
In this paper, we have presented the Noether symmetries of flat FRW spacetime in the context of a new action in Teleparallel Gravity which we construct it based on $f(R)$ version. This modified action contains a coupling between scalar field potential and magnetism. Also, we introduce an innovative approach (B.N.S. Approach) for exact solutions which carry more conserved currents than Noether approach. By data analysis of the exact solutions, obtained from Noether approach, late time acceleration and phase crossing are realized, and some deep connections with observational data such as the age…
In the present work, we consider a model with a fermionic field that is non-minimally coupled to gravity in the framework of teleparallel gravity. In order to determine forms of the coupling and potential function of fermionic field for the considered model, we use Noether symmetry approach. By applying this approach, for the Friedman-Robertson-Walker metric, we obtain respective potential and coupling function as a linear and power-law form of the bilinear $Ψ$. Further we search the exact cosmological solution of the model. It is shown that the fermionic field plays role of the dark energy.
We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are invariant under point transformations in a cosmological background and we use the symmetries of these models to reduce the dynamics of the system in order to find analytical solutions.
A gravitational theory of a scalar field non-minimally coupled with torsion and boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of Noether Gauge Symmetry Approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.
In this paper, we study early-time inflation and late-time acceleration of the universe by non-minimally coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with that of the 3+1 dimensional teleparallel gravity under Noether symmetry approach. And we see that the study explains early-time inflation and late-time acceleration of the universe.
In this paper, in the framework of teleparallel gravity we consider scalar tensor theories of gravity in which scalar fields are nonminimal coupled to torsion scalar. Noether symmetry of the Lagrangian of such a theory for the Friedman-Robertson-Walker spacetime is used to determine the explicit forms for the coupling function and for the potential, and it is shown that both must be power-law forms as a functions of the scalar field. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. It is shown that the equatio…
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper we use the Noether's symmetry approach for a modified Teleparallel theory of gravity labelled as $f(T,B)$ gravity where $T$ is the scalar torsion and $B$ the boundary term. Using the Noether's theorem, we were able to find exact spherically symmetric solutions for different forms of the function $f(T,B)$ coming from the Noether's symmetries.
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…
All degrees of freedom related to the torsion scalar can be explored by analysing, the $f(T,T_G)$ gravity formalism where, $T$ is a torsion scalar and $T_G$ is the teleparallel counterpart of the Gauss-Bonnet topological invariant term. The well-known Noether symmetry approach is a useful tool for selecting models that are motivated at a fundamental level and determining the exact solution to a given Lagrangian, hence we explore Noether symmetry approach in $f(T,T_G)$ gravity formalism with three different forms of $f(T,T_G)$ and study how to establish nontrivial Noether vector form for each o…
We review the current status of the Lorentz covariance in teleparallel and modified teleparallel theories of gravity, and discuss the controversial features of the different approaches. We also revisit the issue of the remnant Lorentz gauge symmetries in $f(T)$ gravity.
There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imp…
A 2D symmetric teleparallel gravity model is given by a generic 4-parameter action that is quadratic in the non-metricity tensor. Variational field equations are derived. A class of conformally flat solutions is given. We also discuss static and cosmological solutions.
We study dynamics of generalized tachyon scalar field in the framework of teleparallel gravity. This model is an extension of tachyonic teleparallel dark energy model which has been proposed in [26]. In contrast with tachyonic teleparallel dark energy model that has no scaling attractors, here we find some scaling attractors which means that the cosmological coincidence problem can be alleviated. Scaling attractors present for both interacting and non-interacting dark energy, dark matter cases.
We construct a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to the unimodular gravity (as well as the Einstein gravity) at the non-linear level.
We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analogue of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed.
We consider the cosmology of a brane-world scenario in the framework of teleparallel and $f(T)$ gravity in a way that matter is localized on the brane. We show that the cosmology of such branes is different from the standard cosmology in teleparallelism. In particular, we obtain a class of new solutions with a constant five-dimensional radius and cosmologically evolving brane in the context of constant torsion $f(T)$ gravity.
Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar $T$, the boundary term $B$ and a scalar field $ϕ$. The goal is to classify possible new polarizations generalizing results presented in Ref.[15]. We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same p…
We consider the quantization of matter fields in a background described by the teleparallel equivalent to general relativity. The presence of local Lorentz and gauge symmetries gives rise to different coupling prescriptions, which we analyse separately. As expected, quantum matter fields produce divergences that cannot be absorbed by terms in the background action of teleparallel equivalent to general relativity. Nonetheless, the formulation of teleparallel gravity allows one to find out the source of the problem. By imposing local Lorentz invariance after quantization, we show that a modified…
Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel gravity and its generalizations can be found in the literature, especially regarding their local Lorentz invariance. We describe how these misunderstandings may have arisen and attempt to clarify the situation. In particular, the central point of confusion in the literature appears to be related to the inertial spin connection in teleparallel gravity models…
The non-minimally coupled symmetric teleparallel gravity with electromagnetic field
本文构造了四维中与电磁场非最小耦合的对称平行引力模型，首次推导其场方程，并在重合规范下得到若干球对称静态解。
The basics of teleparallel gravity and its extensions are reviewed with particular emphasis on the problem of Lorentz-breaking choice of connection in pure-tetrad versions of the theories. Various possible ways to covariantise such models are discussed. A by-product is a new form of $f(T)$ field equations.
We study teleparallel gravity in five-dimensional spacetime with particular discussions on Kaluza-Klein (KK) and braneworld theories. We directly perform the dimensional reduction by differential forms. In the braneworld theory, the teleparallel gravity formalism in the Friedmann-Lemaître-Robertson-Walker cosmology is equivalent to GR due to the same Friedmann equation, whereas in the KK case the reduction of our formulation does not recover the effect as GR of 4-dimensional spacetime.
Generalised Proca theories of gravity represent an interesting class of vector-tensor theories where only three propagating degrees of freedom are present. In this work, we propose a new teleparallel gravity analog to Proca theories where the generalised Proca framework is extended due to the lower order nature of torsion based gravity. We develop a new action contribution and explore the example of the Friedmann equations in this regime. We find that teleparallel Proca theories offer the possibility of a much larger class of models in which do have an impact on background cosmology.
In this work we use the theory of Teleparallelism Equivalent to General Relativity based in non-commutative space-time coordinates. In this context, we write the corrections of the Schwarzschild solution. As a important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the non-commutativity of space-time. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.
We study gauge properties of the general teleparallel theory of gravity, defined in the framework of Poincare gauge theory. It is found that the general theory is characterized by two kinds of gauge symmetries: a specific gauge symmetry that acts on Lagrange multipliers, and the standard Poincare gauge symmetry. The canonical generators of these symmetries are explicitly constructed and investigated.
We study logamediate inflation in the context of $f(T)$ teleparallel gravity. $f(T)$-gravity is a generalization of the teleparallel gravity which is formulated on the Weitzenböck spacetime, characterized by the vanishing curvature tensor (absolute parallelism) and the non-vanishing torsion tensor. We consider an $f(T)$-gravity model which is sourced by a canonical scalar field. Assuming a power-law $f(T)$ function in the action, we investigate an inflationary universe with a logamediate scale factor. Our results show that, although logamediate inflation is completely ruled out by observationa…
Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known i…
It is well known that one cannot apply a conformal transformation to $f(T)$ gravity to obtain a minimally coupled scalar field model, and thus no Einstein frame exists for $f(T)$ gravity. Furthermore nonminimally coupled "teleparallel dark energy models" are not conformally equivalent to $f(T)$ gravity. However, it can be shown that $f(T)$ gravity is conformally equivalent to a teleparallel phantom scalar field model with a nonminimal coupling to a boundary term only. In this work, we extend this analysis by considering a recently studied extended class of models, known as $f(T,B)$ gravity, wh…
Recently, a new choice of variables was identified to understand how the quantum group structure appeared in three-dimensional gravity [1]. These variables are introduced via a canonical transformation generated by a boundary term. We show that this boundary term can actually be taken to be the volume of the boundary and that the new variables can be defined in any dimension greater than three. In addition, we study the associated metric and teleparallel formalisms. The former is a variant of the Henneaux--Teitelboim model for unimodular gravity. The latter provides a non-Abelian generalizatio…
Symmetric teleparallel gravity (STG) is an alternative description of the gravitational field as an effect of the nonmetricity rather than the curvature of the spacetime. For an specific choice of the symmetric teleparallel lagrangian, the STG dynamics is equivalent to the general relativity (GR), and it is called Symmetric teleparallel equivalent to general relativity (STEGR). We propose a local Lorentz violating dynamics in the gravitational sector in the STEGR framework. The Lorentz violation is trigged by the vacuum expectation value (vev) of the well-known bumblebee field, whose vev coupl…
We consider modified teleparallel gravity, (f(T) gravity), as a framework to explain the present accelerated expansion of the universe. The matter component is assumed to be cold dark matter. To find the explicit form of the function $f$, we utilize generalized Noether theorem and use generalized vector fields as variational symmetries of the corresponding Lagrangian. We study the cosmological consequences of the obtained results.
Homogeneous and isotropic cosmology in general teleparallel gravity
本文分类均匀各向同性远平行几何的五类平直仿射联络解，并推导多类广义远平行引力理论的宇宙学动力学，揭示其可约化关系及至多两个新标量自由度。
We study the conservation laws associated with the asymptotic Poincare symmetry of spacetime in the general teleparallel theory of gravity. Demanding that the canonical Poincare generators have well defined functional derivatives in a properly defined phase space, we obtain the improved form of the generators, containing certain surface terms. These terms are shown to represent the values of the related conserved charges: energy-momentum and angular momentum.
During the conference "Teleparallel Universes in Salamanca", we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 99 (2019) 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge theory for the translation group were put forward. This triggered a discussion about the arguments on which those criticisms were based, whose output is described in the present paper. The main conclusion is that, to a great extent, those arguments are incorrect, and lack mathematical and physical support.
We study conditions on a generic connection written in terms of first-order derivatives of the vielbein in order to obtain (possible) equivalent theories to Einstein Gravity. We derive the equations of motion for these theories which are based on the new connections. We recover the Teleparallel Gravity equations of motion as a particular case. The analysis of this work might be useful to Double Field Theory to find other connections determined in terms of the physical fields.
Teleparallel gravity
本文简要介绍Teleparallel引力理论，该理论通过无曲率联络的挠率中介引力，并概述其常见理论类别，侧重实际计算。
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 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…
The Hamilton equations in $f(T)$ teleparallel gravity and in New General Relativity
本研究推导协变形式下扩展远平行引力理论的哈密顿函数与方程，对比发现$f(T)$引力和新广义相对论均可退化为广义相对论的远平行等价理论，但二者与$f(R)$引力的哈密顿方程存在显著差异。
We analyze the construction of conformal theories of gravity in the realm of teleparallel theories. We first present a family of conformal theories which are quadratic in the torsion tensor and are constructed out of the tetrad field and of a scalar field. For a particular value of a coupling constant, and in the gauge where the scalar field is restricted to assume a constant value, the theory reduces to the teleparallel equivalent of general relativity, and the tetrad field satisfies Einstein's equations. A second theory is formulated out of the tetrad field only, and is not equivalent to the…
Gravitational wave in symmetric teleparallel gravity with different connections
本文在对称远平行引力框架下，针对空间平坦宇宙的三个分支及不同联络，系统分析并比较了张量型与非张量型引力波的传播行为和稳定性，模型同时覆盖f(Q)理论与标量场-非度规标量非最小耦合情形。
In this paper, we present the Noether symmetries of a class of the Bianchi type I anisotropic model in the context of f(T) gravity. By solving the system of equations obtained from the Noether symmetry condition, we obtain the form of f(T) as a teleparallel form. This analysis shows that teleparallel gravity has the maximum number of Noether symmetries. We derive the symmetry generators and show that there are five kinds of symmetries, including time and scale invariance under metric coefficients. We classify the symmetries and we obtain the corresponding invariants.
We give a pedagogical introduction into the field of (modified) teleparallel theories of gravity. Our presentation is fairly self-contained. In particular, we carefully explain the basic principles of metric-affine approaches to gravity. This contribution is based on our talk "Teleparallel gravity, its modifications, and the local Lorentz invariance" at the 9th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics in Belgrade, September 2017.
Geometry and covariance of symmetric teleparallel theories of gravity
本文研究对称远平行引力理论的几何基础与运动方程推导，揭示协变化背后的四元组结构，并证明协变化在运动方程中的唯一物理效应是要求能量-动量张量满足协变守恒定律，同时引入协变守恒远平行四元组。
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. So 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 transformat…
We discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in teleparallel gravity and study conformal torsion gravity. We explicitly demonstrate that a power-law acceleration (including the $Λ$CDM universe) as well as the de Sitter expansion of the universe can be realized in extended teleparallel gravity with a conformal scalar field, and that pure teleparallel gravity with a conformal scalar field can lead to the $Λ$CDM mod…
The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
本研究在TEGR和STEGR框架下，利用Noether流分析平面引力波的能动量，发现特定条件下流为零，对应等价原理，并区分正零能量情况。
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 this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for $f(T)$ gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz br…
Free fall in modified symmetric teleparallel gravity
本文研究了修正的对称遥平行引力中的自由落体与等效原理，指出该理论虽不服从Weinberg意义上的等效原理，但自由下落测试粒子必然沿包含Levi-Civita联络的度规测地线运动。
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