We mainly focus on the idea that the dynamics of the whole universe may be understood by making use of torsion [Formula: see text] and curvature [Formula: see text] at the same time. The [Formula: see text]-gravity can be considered as a fundamental gravitational theory describing the evolution of the universe. The model can produce the unification of the general relativity (GR), teleparallel gravity (TPG), [Formula: see text]-gravity and [Formula: see text]-gravity theories. For this purpose, the corresponding Lagrangian density is written in terms of an arbitrary function of the torsion and curvature scalars. Furthermore, we use the absence/existence puzzle of relativistic neutron stars and thermodynamical laws as constraining tools for the new proposal.
We present here a new modified gravitation theory for the galactic dark energy effect by using a general Lagrangian density which is represented by an arbitrary function f(T, [Formula: see text], X) where T describes the torsion scalar in teleparallel gravity while X shows the kinetic scalar field energy. While the function is in general form, once reduced, the model can be transformed into some of the other well-known gravitation theories. After deriving the corresponding field equations and considering the flat Friedmann–Robertson–Walker type universe which is filled with ordinary cosmic matter, we discuss both the non-equilibrium and equilibrium profiles of galactic thermodynamics. We find that there exists an equilibrium picture of thermodynamics. Additionally, we also generalize ordinary f(T, [Formula: see text], X) model’s action to the case in which there exists an interaction between the chameleon and scalar fields.
In this study, the validity of the generalized second law of thermodynamics (GSLT) has been investigated in F(R, G) gravity. We consider that the boundary of the universe is surrounded by an apparent horizon in the spatially flat Friedmann–Robertson–Walker (FRW) universe, and we take into account the Hawking temperature on the horizons. The unified solutions of the field equations corresponding to gravity theory have been applied to the validity of the GSLT frame, and in this way, both the solutions have been verified and all the expansion history of the universe has been shown in a unified picture.
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