Abstract
The present study is elaborated to investigate the validity of thermodynamical laws in a modified teleparallel gravity based on higher-order derivative terms of torsion scalar. For this purpose, we consider spatially flat FRW model filled with perfect fluid matter contents. Firstly, we explore the possibility of existence of equilibrium as well as non-equilibrium picture of thermodynamics in this extended version of teleparallel gravity. Here, we present the first law and the generalized second law of thermodynamics (GSLT) using Hubble horizon. It is found that non-equilibrium description of thermodynamics exists in this theory with the presence of an extra term called as entropy production term. We also establish GSLT using the logarithmic corrected entropy. Further, by taking the equilibrium picture, we discuss validity of GSLT at Hubble horizon for two different F models. Using Gibbs law and the assumption that temperature of matter within Hubble horizon is similar to itself, We use different choices of scale factor to discuss the GSLT validity graphically in all scenarios. It is found that the GSLT is satisfied for a specified range of free parameters in all cases.
Highlights
Teleparallel gravity is regarded as one of the interesting alternative to Einstein’s gravity (GR) in which torsional formulation provides the gravitational source instead of curvature scalar structure of GR [45,46,47,48,49,50]
A variety of extended versions of this theory have been presented in literature like f (T ) gravity where a generic function of torsion scalar replaces the simple torsion scalar term in the Lagrangian density [39,40,41,42,43,44]
Another different version of this theory has been proposed by Kofinas and Saridakis [51,52,53,54] where they introduced a new term TG called teleparallel equivalent to Gauss–Bonnet term and further, they extended this theory to a more general case named as f (T, TG ) theory
Summary
Teleparallel gravity is regarded as one of the interesting alternative to Einstein’s gravity (GR) in which torsional formulation provides the gravitational source instead of curvature scalar structure of GR [45,46,47,48,49,50]. Another different version of this theory has been proposed by Kofinas and Saridakis [51,52,53,54] where they introduced a new term TG called teleparallel equivalent to Gauss–Bonnet term and further, they extended this theory to a more general case named as f (T, TG ) theory Another significant modification is considered by Harko et al [55,56] by including a non-minimal interaction of torsion scalar with matter field in the action. The generalization of torsion based theories obtained by including higher-order derivative terms like (∇T ) and T can be expressed by the following action [60]: A. where Sm(eρA, ψm) denotes the ordinary matter part of action. The field equations take the following form: FT H 2 + (24H 2 FX1 + FX2 )(3H H + H )H
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