Modified teleparallel gravity with higher-derivative torsion terms

Abstract

We construct $F(T,{\left(\nabla T\right)}^2,\square T)$ gravitational modifications, which are novel classes of modified theories arising from higher-derivative torsional terms in the action, and are different than their curvature analogue. Applying them in a cosmological framework we obtain an effective dark energy sector that comprises of the novel torsional contributions. We perform a detailed dynamical analysis for two specific examples, extracting the stable late-time solutions and calculating the corresponding observables. We show that the thermal history of the universe can be reproduced, and it can result in a dark-energy dominated, accelerating universe, where the dark-energy equation-of-state parameter lies in the quintessence regime, or may exhibit the phantom-divide crossing during the cosmological evolution. Finally, the scale factor behaves asymptotically either as a power-law or as an exponential, in agreement with observations.

13 pages, 6 figures, 2 Tables, version published in PRD

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• Can Horndeski Theory be recast using Teleparallel Gravity?
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• Gravitational Waves in Modified Teleparallel Theories
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Gravitational Waves in Higher Order Teleparallel Gravity
• Kinetic Scalar Curvature Extended $f(R)$ Gravity
• Scattering of Fermions by Gravitons
• Phase Space description of Nonlocal Teleparallel Gravity
• Energy conditions in f(T) gravity with higher-derivative torsion terms
• Thermodynamics in a Modified Gravity Involving Higher-Order Torsion Derivative Terms
• Revisiting $f(R)$ gravity's rainbow: Inflation and primordial fluctuations
• Focusing conditions for extended teleparallel gravity theories
• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity