Teleparallel equivalent of Gauss-Bonnet gravity and its modifications

By G. Kofinas, Emmanuel N. Saridakis. 2014

207 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d0616b83a599ec066b6dad38f5a9a86a8c1c1ad0

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Citations in the corpus

f(T,𝒯) gravity and cosmology (2014, background): “Additionally, note that if one starts from TEGR, but instead of the f(R) is inspired by higher-curvature modifications of General Relativity, one can construct higher-order torsion gravity, such as the f(T, TG) paradigm [56, 57], which also presents interesting cosmological behavior.”
Cosmological perturbations in modified teleparallel gravity models (2018, background): “[15, 16, 17]) additional scalar fields in the action (see [7] and Section 9).”
Dynamical behavior in f (T, TG) cosmology (2014, methodology): “The cosmological applications of f T T ( , ) G gravity prove to be very interesting [55].”
f(T) teleparallel gravity and cosmology (2015, methodology): “Varying the action (771) in terms of the vierbein, after various steps, one finally obtains [587]”
Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “These include, for instance, the so-called teleparallel Gauss-Bonnet gravity [127, 128] inspired by analogous work in the curvature approach [129], where the following Lagrangian was considered”