Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions

Abstract

We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies.

15 pages, 2 figures, 1 table; slightly revised version

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Cited by in corpus (49)

• Teleparallel Gravity: From Theory to Cosmology
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Teleparallel Palatini theories
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• Can Horndeski Theory be recast using Teleparallel Gravity?
• New classes of modified teleparallel gravity models
• Hamiltonian formalism for f(T) gravity
• Constraining f(T) teleparallel gravity by Big Bang Nucleosynthesis
• Cosmological viable models in $f(T,B)$ gravity as solutions to the $H_0$ tension
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Conformal Gravity and Transformations in the Symmetric Teleparallel Framework
• Modified gravity: a unified approach
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• Cosmological bouncing solutions in extended teleparallel gravity theories
• Quest for the extra degree of freedom in f(T) gravity
• Effective gravitational coupling in modified teleparallel theories
• Nonlocal Teleparallel Cosmology
• Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term
• Symmetry and Equivalence in Teleparallel Gravity
• Energy Constraints and Phenomenon of Cosmic Evolution in $f(T,B)$ Framework
• Generalized Second Law of Thermodynamic in Modified Teleparallel Theory
• Modified gravity: a unified approach to metric-affine models
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• McVittie solution in f(T) gravity
• Scalarized Black Holes in Teleparallel Gravity
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• Generalised nonminimally gravity-matter coupled theory
• Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A${}^{\star }$ observations
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity
• Scattering of Fermions by Gravitons
• String-inspired Teleparallel Cosmology
• Observational Constraints and Cosmographic Analysis of $f(T,T_G)$ Gravity and Cosmology
• Noether Symmetries in $f(T,T_G)$ Cosmology
• General Teleparallel Modifications of Schwarzschild Geometry
• Dynamical Complexity in Teleparallel Gauss-Bonnet Gravity
• Modified Teleparallel Gravity induced by quantum fluctuations
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Thermodynamics in a Modified Gravity Involving Higher-Order Torsion Derivative Terms
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Constraining $f(T,B,T_G,B_G)$ gravity by dynamical system analysis
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity
• Focusing conditions for extended teleparallel gravity theories
• Gauge invariant perturbations of $F(T,T_G)$ Cosmology
• The Effect of Modified Dispersion Relation on Dumb Holes
• Growth factor in teleparallel Gauss-Bonnet gravity