A geometric view on local Lorentz transformations in teleparallel gravity

Hohmann, Manuel

doi:10.48550/arxiv.2112.15173

Cited by 4 publications

(6 citation statements)

References 46 publications

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“…It is this condition that forces the distinction between curvature and teleparallel based connections. Finally, note that for a given metric-affine geometry, a tetrad, in general, exists only locally, and that global tetrads exist only if the spacetime manifold M is parallelizable; this fact can be understood by applying the theory of fiber bundles [50].…”

Section: Relation To Metric and Connectionmentioning

confidence: 99%

Teleparallel gravity: from theory to cosmology

et al. 2023

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Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein’s other theory of gravity. In this Review, we give a comprehensive introduction to how teleparallel geometry is developed as a gauge theory of translations together with all the other properties of gauge field theory. We also related 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 behaviors for other scenarios, such as quantum gravity. After setting this foundation, we describe the plethora of modified teleparallel theories of gravity that have been proposed in the literature. We attempt to connect them together into general classes of covariant gravitational theories. Of particular interest, we highlight the recent proposal of a teleparallel analogue of Horndeski gravity which offers the possibility of reviving all of the regular Horndeski contributions. In the second part of the Review, we first survey works in teleparallel astrophysics literature where we focus on the open questions in this regime of physics. We then discuss the cosmological consequences for the various formulations of teleparallel gravity. We do this at background level by exploring works using various approaches ranging from dynamical systems to Noether symmetries, and more. Naturally, we then discuss perturbation theory, firstly by giving a concise approach in which this can be applied in teleparallel gravity theories and then apply it to a number of important theories in the literature. Finally, we examine works in observational and precision cosmology across the plethora of proposal theories. This is done using some of the latest observations and is used to tackle cosmological tensions which may be alleviated in teleparallel cosmology. We also introduce a number of recent works in the application of machine learning to gravity, we do this through deep learning and Gaussian processes, together with discussions about other approaches in the literature.

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Section: Relation To Metric and Connectionmentioning

confidence: 99%

Teleparallel gravity: from theory to cosmology

et al. 2023

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“…Neglecting this fact would severely constrain the applicability of the teleparallel geometry [14,39]. A constructive approach how to obtain the Weitzenböck gauge follows from its geometric interpretation [40].…”

Section: Introductionmentioning

confidence: 99%

Perturbations in non-flat cosmology for f(T) gravity

et al. 2023

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The study of cosmological perturbation theory in f(T) gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary f(T) models, when the most general homogeneous and isotropic background tetrads are used. We also identify propagating modes in this setup, and relate this with the case of a flat cosmology.

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“…The resulting theory (50)-( 54) is known as the covariant teleparallel gravity [15,16] It is worthwhile to mention that the representation (53) was consistently used by Blixt et al [4] for the thorough analysis of the degrees of freedom issue in the teleparallel gravity theory; see also the related work on the Lorentz symmetry in the teleparallel gravity by Hohmann [8,9].…”

Section: Composite Gauge Fieldsmentioning

confidence: 99%

Conservation laws in gauge gravity theory

Obukhov¹

2022

Preprint

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We analyse the conservation laws in the gauge gravity theory which are derived for the general class of gravitational models with the action invariant under the local Poincaré and the diffeomorphism group. The consistent Noether-Lagrange formalism is developed, revealing the important role of the auxiliary Goldstone and Stueckelberg fields, with the help of which we construct the composite gauge fields that have a clear geometrical and physical meaning.

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A geometric view on local Lorentz transformations in teleparallel gravity

Cited by 4 publications

References 46 publications

Teleparallel gravity: from theory to cosmology

Teleparallel gravity: from theory to cosmology

Perturbations in non-flat cosmology for f(T) gravity

Conservation laws in gauge gravity theory

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