We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.
Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry where scalar-tensor theories are considered in this torsional framework. Being teleparallel gravity of lower order in dynamics, this turns out to be more general than metric Horndeski gravity. In other words, the class of teleparallel Horndeski gravity models is much broader than the standard metric one. In this work, we explore constraints on this wide rang…
We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General …
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.
In this paper we consider the parity violating gravity model within the framework of teleparallel gravity. The parity violations are caused by the couplings of a scalar field to the scalar invariants which are parity-odd and quadratic in the torsion tensor. Totally there are two such type independent invariants, and one of them is the Nieh-Yan density. Through investigations on the cosmological perturbations of this model, we find that in general it suffers from the difficulties of ghost instability in the scalar and vector perturbations. But in the special case only the coupling to the Nieh-Y…
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.
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 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…
Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly un…
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…
Generators of Internal Lorentz Transformations and of General Affine Coordinate Transformations in Teleparallel Theory of (2+1)-Dimensional Gravity --- Cases with Static Circularly Symmetric Space-Times---
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.
虽然用经典实验无法区分广义相对论和遥平行引力，但通过量子引力效应可以区分它们。这些效应激发了广义相对论引入非定域变形的动机，类似的效应也有望在遥平行引力中发生。在这里，我们研究Telepallel引力的非局部变形及其宇宙学解。我们观察到，非定域遥平行引力（类似于非定域广义相对论）与目前由SNe Ia + BAO + CC + $H_0$观测得到的宇宙学数据是一致的。沿着这条轨道，未来探索非定域效应的实验可以用来检验广义相对论或远程平行引力是否给出了引力相互作用的最一致的图景。
Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent teleparallel theories that respect certain physical conditions such as local Lorentz invariance. We first use teleparallel gravity to formulate a teleparallel equivalent of general relativity which is dynamically equivalent to general relativity but which may have different beh…
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…
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…
Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
我们证明了在广义相对论的遥平行等价中，狄拉克旋量场与引力场的耦合是相容的。对于任意的SO（3，1）联络，旋量场与引力场的耦合有两种可能。Y. N. Obukhov和J. G. Pereira在论文{ \it Metric-affine approach to teleparallel gravity} [gr-qc/0212080]中只在一个特定耦合的框架中发生。通过采用替代耦合，一致性问题消失了。
在“萨拉曼卡远程平行宇宙”会议期间，我们注意到最近的一篇论文[M。丰塔尼尼，E. Huguet和M. Le Delliou，Phys. Rev. D 99（2019）064006]，其中对平行引力作为平移群的规范理论的解释提出了一些批评。这引发了对这些批评所依据的论点的讨论，本文件介绍了讨论的结果。主要结论是，在很大程度上，这些论点是不正确的，缺乏数学和物理支持。
