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.

The Higgs mechanism for gravity, as proposed by 't Hooft in arXiv: 0708.3184 [hep-th], can be augmented by including determinantal invariants. We analyze the effects of determinantal invariants in such a set up. We find that the part of the potential that depends on the determinantal invariants, if obtains a specific exponential form in terms of its argument, may not affect the graviton mass calculated.

In order to evaluate energy and momentum components associated with two different black hole models, i.e. the electric and magnetic black holes, we use the Møller energy-momentum prescriptions both in Einstein's theory of general relativity and the teleparallel gravity. We obtain the same energy and momentum distributions in both of these different gravitation theories. The energy distribution of the electric black hole depends on the mass M and the magnetic black hole energy distribution depends on the mass M and charge Q. In the process, we notice that (a) the energy obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling parameter, which means that it is valid not only in teleparallel equivalent of general relativity but also in any teleparallel model, (b) our results also sustains the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime, and (c) the results obtained support the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum.

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In this work, in order to compute energy and momentum distributions (due to matter plus fields including gravitation) associated with the Brans-Dicke wormhole solutions we consider Møller's energy-momentum complexes both in general relativity and the teleparallel gravity, and the Einstein energy-momentum formulation in general relativity. We find exactly the same energy and momentum in three of the formulations. The results obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling parameter, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum. (c) The results calculated supports the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of matter and all non-gravitational fields.