Generalized second law of thermodynamic in modified teleparallel theory

The European Physical Journal C, Jul 2017

This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term \(B=2\nabla _{\mu }T^{\mu }\). This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon.

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Generalized second law of thermodynamic in modified teleparallel theory

Eur. Phys. J. C Generalized second law of thermodynamic in modified teleparallel theory M. Zubair 0 Sebastian Bahamonde 1 Mubasher Jamil 2 0 Department of Mathematics, COMSATS Institute of Information Technology Lahore , Lahore , Pakistan 1 Department of Mathematics, University College London , Gower Street, London WC1E 6BT , UK 2 Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST) , H-12, Islamabad , Pakistan This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term B = 2??T ?. This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon. 1 Introduction The rapid growth of observational measurements on expansion history reveals the expanding paradigm of the universe. This fact is based on accumulative observational evidence mainly from Type Ia supernova and other renowned sources [ 1?3 ]. The expanding phase implicates the presence of a repulsive force which compensates the attractiveness property of gravity on cosmological scales. This phenomenon may be translated as the existence of exotic matter components and most acceptable understanding for such enigma is termed dark energy (DE); it has a large negative pressure. Various DE models and modified theories of gravity have been proposed to incorporate the role of DE in cosmic expansion history (for reviews see [4?6]). In contrast to Einstein?s relativity and its proposed modifications where the source of gravity is determined by curvature scalar terms, another formulation has been presented which comprises a torsional formulation as gravity source [ 7?11 ]. This theory is labeled TEGR (teleparallel equivalent of general relativity) and it is determined by a Lagrangian density involving a zero curvature Weitzenb?ck connection instead of a zero torsion Levi-Civita connection with the vierbein as a fundamental tool. The Weitzenb?ck connection is a specific connection which characterizes a globally flat space-time endowed with a non-zero torsion tensor. Using that connection, one can construct an alternative and equivalent theory of GR. The latter appears, since the scalar torsion 2 only differs by a boundary term B = e ??(eT ?) with the scalar curvature by the relationship R = ?T + B, making the two variations of the Einstein?Hilbert and TEGR actions the same. Thus, these two theories have the same field equations. However, these two theories have different geometrical interpretations, since in TEGR the torsion acts as a force; meanwhile in GR, the gravitational effects are understood due to the curved space-time. TEGR is then further extended to a generalized form by the inclusion of a f (T ) function in the Lagrangian density (as f (R) is the extension of GR) and it has been tested cosmologically by numerous researchers [12?14]. It is important to mention that f (T ) and f (R) are no longer equivalent theories, and in order to consider the equivalent teleparallel theory of f (R), one needs to consider a more generalized function f (T , B), incorporating the boundary term in the action [15]. In [16], the authors studied some cosmological features (reconstruction method, thermodynamics and stability) within f (T , B) gravity and, in [17], some cosmological solutions were found using the Noether symmetry approach. Additionally, it has been proved that when one considers Gauss?Bonnet higher order terms, an additional boundary term BG (related to the contorsion tensor) needs to be introduced to find the equivalent teleparallel modified Gauss?Bonnet f (R, G) theory [18]. Later, Harko et al. [19] proposed a comprehensive form of this theory by involving a non-minimal torsion matter interaction in the Lagrangian density. In Ref. [20], Zubair and Waheed recently have investigated the validity of energy constraints for some specific f (T ) models and discussed the feasible bounds of involved arbitrary parameters. They also discussed the validity of the generalized second law of thermodynamic in the cosmological constant regime [21]. Another very much studied approach in modified theories of gravity is to change the matter content of the universe by adding a scalar field in the matter sector. These models have been considered several times in cosmology, using different kinds of scalar fields such as quintessence, quintom, k-essence, etc. (see [22?24]). Moreover, we can also extend that idea by (...truncated)


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M. Zubair, Sebastian Bahamonde, Mubasher Jamil. Generalized second law of thermodynamic in modified teleparallel theory, The European Physical Journal C, 2017, pp. 472, Volume 77, Issue 7, DOI: 10.1140/epjc/s10052-017-5043-y