Teleparallel equivalent of Gauss-Bonnet gravity and its modifications

Abstract

Inspired by the teleparallel formulation of General Relativity, whose Lagrangian is the torsion invariant T, we have constructed the teleparallel equivalent of Gauss-Bonnet gravity in arbitrary dimensions. Without imposing the Weitzenbock connection, we have extracted the torsion invariant T_G, equivalent (up to boundary terms) to the Gauss-Bonnet term G. T_G is constructed by the vielbein and the connection, it contains quartic powers of the torsion tensor, it is diffeomorphism and Lorentz invariant, and in four dimensions it reduces to a topological invariant as expected. Imposing the Weitzenbock connection, T_G depends only on the vielbein, and this allows us to consider a novel class of modified gravity theories based on F(T,T_G), which is not spanned by the class of F(T) theories, nor by the F(R,G) class of curvature modified gravity. Finally, varying the action we extract the equations of motion for F(T,T_G) gravity.

10 pages, version to appear in Phys.Rev.D. The general equations of motion have been derived, the cosmological applications are moved to a separate publication

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Cited by in corpus (38)

• $f(T,\mathcal{T})$ gravity and cosmology
• Static Spherically Symmetric Wormholes in $f(R,T)$ Gravity
• Modified cosmology from extended entropy with varying exponent
• Modified cosmology through spacetime thermodynamics and Barrow horizon entropy
• Cosmological applications of $F(T,T_G)$ gravity
• Testing wormhole solutions in extended gravity through the Poynting-Robertson effect
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• Cosmological bouncing solutions in f(T,B) gravity
• Dynamical features of scalar-torsion theories
• Remnant group of local Lorentz transformations in f(T) theories
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Cosmology in cubic and $f(P)$ gravity
• Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
• Late-time cosmology with phantom dark-energy in $f(Q)$ gravity
• Non-Local Gravity Cosmology: an Overview
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• Self-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
• FRW in quadratic form of $f(T)$ gravitational theories
• Coincident f(Q) gravity: black holes, regular black holes and black bounces
• Nonlocal Teleparallel Cosmology
• Geodesic Deviation Equation in $f(T)$ gravity
• Thick brane in f(T,B) gravity
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Gravitationally Induced Particle Production through a Nonminimal Torsion-Matter Coupling
• Alleviating $H_0$ tension in scalar-tensor and bi-scalar-tensor theories
• Big Bang Nucleosynthesis constraints on $f(T,T_G)$ gravity
• Unimodular $f(G)$ gravity
• Dynamics of Bianchi $V{I}_h$ Universe with Bulk Viscous Fluid in Modified Gravity
• Can $f(R)$ gravity isotropize a pre-bounce contracting universe?
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Aether-quasi-dilaton massive gravity
• Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions
• Brane cosmology in teleparallel and $f(T)$ gravity
• Energy Constraints for Evolving Spherical and Hyperbolic Wormholes in $f(R,T)$ Gravity
• Phenomenological modification of horizon temperature
• Perturbations In Some Dark Energy Models
• Generalized Hodge dual for torsion in teleparallel gravity
• A proof of the Chern-Gauss-Bonnet theorem for indefinite signature metrics using analytic continuation