Chapter to appear in "Handbook of Spacetime", edited by A. Ashtekar and V. Petcov (Springer, Berlin, 2013). V2: misprints corrected, references updated
Teleparallel gravity, a gauge theory for the translation group, turns up as fully equivalent to Einstein's general relativity. In spite of this equivalence, it provides a whole new insight into gravitation. It breaks several paradigms related to the geometric approach of general relativity, and introduces new concepts in the description of the gravitational interaction. The purpose of this chapter is to explore some of these concepts, as well as discuss possible consequences for gravitation, mainly those that could be relevant for the quantization of the gravitational field.
Arbitrary generalization to the teleparallel equivalent of general relativity loses local Lorentz invariance to reparametrize the orthonormal coordinate system and gives rise to asymmetry field equations. We investigate consequences of local Lorentz violation to primordial fluctuations in extended single field inflationary models based on the scalar-tensor formulation of the torsion scalar $T$ that effectively includes $f(T)$ gravity as a special case. We show that despite some asymmetry part of the field equations are removed in a spatially homogeneous and isotropic cosmic background, no subh…
At the time it celebrates one century of existence, general relativity---Einstein's theory for gravitation---is given a companion theory: the so-called teleparallel gravity, or teleparallelism for short. This new theory is fully equivalent to general relativity in what concerns physical results, but is deeply different from the conceptual point of view. Its characteristics make of teleparallel gravity an appealing theory, which provides an entirely new way to think the gravitational interaction.
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological field equation from the metric-dependent constitutive law. We show here that GR allows for a premetric formulation, too. For this purpose, we apply the teleparallel approach of gravity, which represents GR as a gauge theory based on the translation group. We formulate the metric-free topological field equation and a general linear constitutive la…
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms reside in the metric formulation of general relativity, as the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black …
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…
It is shown that teleparallel $F(T)$ theories of gravity combined with holonomy corrected Loop Quantum Cosmology (LQC) support a Matter Bounce Scenario (MBS) which is a potential alternative to the inflationary paradigm. The Matter Bounce Scenario is reviewed and, according to the current observational data provided by PLANCK's team, we have summarized all the conditions that it has to satisfy in order to be a viable alternative to inflation, such as to provide a theoretical value of the spectral index and its running compatible with the latest PLANCK data, to have a reheating process via grav…
In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric qui…
我们给一个简短的大纲，在第二节。2，规范思想应用于内部（$U(1),\, SU(2),\dots$）和外部（$R^4,\,SO(1,3),\dots$）对称性的历史发展，并强调相应守恒流的根本重要性。在第二节中，3.中子干涉仪在地球引力场中的实验结果，用等效原理解释，可以用加速旋转参考系中的狄拉克方程预言。在这样一个非惯性系中使用狄拉克方程，我们描述了如何在规范理论的方法（见表1）中，存在于包含挠率和曲率的黎曼-嘉当时空中的爱因斯坦-嘉当理论作为最简单的引力理论而产生。这与爱因斯坦在黎曼时空中得出广义相对论的方法相反。以秒为单位。\在图4和图5中，我们考虑了物质的守恒能量-动量流，并对相关的平移子群进行了测量。爱因斯坦的远程平行理论的出现被证明是等价的，为无自旋的物质和电磁，广义相对论。在成功地规范了平移之后，就可以直接规范四维仿射群$R^4 \semidirect GL(4,R)$或它的庞加莱子群$R^4\semidirect SO(1,3)$。我们在第二节中简要报告了这些结果。6（metric-affine geometry）and in Sec. 7（度量仿射场方程（\ref{zeroth}，\ref{first}，\ref{second}））。最后，在SEC。8，我们收集了一些模型，目前正在讨论中，它带来了生命的度量仿射规范框架开发。
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
Probing Quantum Gravity in Stellar Spacetimes: Phenomenological Insights
Mapúa University（马普阿大学）；Eastern Mediterranean University（东地中海大学）；Università degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Salerno - Sezione di Napoli（意大利国家核物理研究所 - 萨莱诺协作组 - 那不勒斯分部）
It is well-known that perturbative quantum gravity is non-renormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this essay, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective r…
This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an attempt to extract the cosmological sector of the full theory. We reconsider the reduction procedure applied to the states of the kinematical Hilbert space, developing a comparative analysis with previous efforts in the literature. We show that the constraints of the model were formerly instantiated in an inconsistent fashion, leading to an overconstrained dynamics and an ill-defined Hilbert space. We then scrutinize alternative implementations…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and nonmetricity participate in the dynamics). We start by revising some mathematical aspects of the metric-affine framework, the way Lovelock and other invariants are extended to it and the construction of a gauge formalism. Then we focus on metric-affine pp-wave geometries and explore solutions of this type for the quadratic metric-affine Lagrangian (with even-pari…
In this paper, we base on the formalism of Symbolic Gauge Theory in the case of General relativity; we calculate the Feynman diagrams for the interaction between harmonic gravitational connections in the topological field theory. These calculations provide insights to interactions between gravity and dark energy. They could, therefore, have important repercussions for current cosmological problems.
Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity
Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Damghan University（达姆甘大学）；Khazar University（哈萨尔大学）；K. N. Toosi University of Technology（科·恩·托伊西理工大学）
