الفهرس 
Chapter 1 Geometric Configurationsand CorrespondingGravityTheoriesOnly 14 pages are availabe for public view
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Abstract
The primary focus of the present study is to investigate the tests of modified gravitation theories in cosmology and astrophysics. The thesis consists of four chapters, 54 figures, 8 tables and ends with a list of references.
Chapter 1:
In this chapter, we briefly review three geometric frameworks. Firstly, is Riemannian ge- ometry, where the field equations in general relativity theory are described, as well as some modified theories in the same geometry such as f(R) and f(R,T). Secondly, the Absolute Parallelism geometry (AP) within the framework of the new general relativity theory. Fi- nally the Parameterized Absolute Parallelism (PAP) geometry, which is used to derive a new theory based on gravity and torsion called f (R, Σ, T ) Gravity. Through this frame- work, we were able to study the Big Rip of cosmological models.
Chapter 2:
In this Chapter, we present a new approach to investigate the Hamiltonian formalism of new general relativity (NGR) by utilizing the constitutive tensor defined through the premetric method. Our procedure involves deriving the canonical momenta that are conjugate to the tetrad field and examining the eigenvalues of the Hessian tensor. To facilitate this analysis, we transform the Hessian tensor into a Hessian matrix using indexation formulas. The properties of the Hessian matrix depend on the values of the free coefficients (ci, i = 1, 2, 3) present in the NGR Lagrangian. Upon investigation, we identify four eigenvalues that are null, corresponding to trivial primary constraints in the temporal component of the momenta. The remaining eigenvalues are organized into four sets with multiplicities of 3, 1, 5, and 3, respectively. These eigenvalues can be set to zero by making different
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choices for the coefficients ci. Consequently, there are nine possible scenarios where one, two, or three sets of eigenvalues are simultaneously forced to vanish. Each case yields a distinct number of primary constraints, consistent with the prior Hamiltonian analysis of NGR conducted by Blixt et al. (2018).
Chapter 3:
This Chapter discusses the field equations of new general relativity, which were devel- oped by Hayashi and Shirafuji. These equations include three free parameters. We applied these field equations to the Friedmann-Robertson-Walker metric in the field of cosmology. Through this application, we derived a family of models that depend on two of the param- eters from the field equations of new general relativity. Certain conditions are imposed on these parameters to ensure compatibility with either the Big Rip or Big Crunch models. These models are considered to be the original relativistic models of relativity theory when the parameters from the field equations are set to unity. By selecting specific values for the field equation parameters and the quadratic deceleration parameter, we obtained exact so- lutions. The field equations yield various types of universes, including radiation, dust, dark energy, vacuum, and phantom universes. Interestingly, these universes are not influenced by the field parameters. Chapter three also discusses energy conditions and the effective potential of the proposed models.
Chapter 4:
In this Chapter, we used the absolute parallelism geometry to obtain a new formula for the Ricci scalar. We consider f (R, Σ, T ) modified theories of gravity, where the gravitational Lagrangian is given by three arbitrary functions of the Ricci scalar R, Ricci torsion scalar Σ, and the trace of the stress-energy tensor T . We obtain the gravitational field equations in the metric formalism. Also, the evolution of the function f(R) with time is studied, and we discuss the parameters that make up the function and impose constraints on these parameters. The solution of the f (R, Σ, T ) gravity equations is obtained under a varying polynomial deceleration parameter. The effect of torsion on cosmological models is also discussed. Physical aspects of the energy density, pressure, and energy conditions of the cosmological models proposed in this article are studied and the evolution of the physical
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parameters is shown in figures. The evolution of the fluid pressure and energy density parameter as a function of redshift has been obtained. The f(R) gravity and f(R, T ) gravity theories as special cases could be inferred from f (R, Σ, T ) gravity. Several special cases have been studied, with illustrations for each case.