Studies of Gravitational Field Equations and Key Results in Relativistic Cosmology
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Abstract
The paper gives a mathematical and theoretical overview of the underlining principles of relativistic cosmology. Starting with the classical Newtonian mechanics and the passage to the dynamic, four-dimensional pseudo-Riemannian manifold of the General Relativity, the analysis proceeds in a systematic manner to create the differential geometry of the General Relativity Gravitational Field Equations. Using the Cosmological Principle of macroscopic homogeneity and isotropy, the mathematical finding of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is shown. Replacing this kinematic model with the field equations gives the Friedmann equations, which serve as the governing different equations of the universe expansion. In addition, this paper compares the specific solutions of these equations at the various cosmological epochs, following the chronological development of the cosmic scale factor through the early radiation era, the then matter era, and the present dark energy era based on the cosmological constant. Finally, in this piece, we find out the success of local geometric field equations that are used to determine the global kinematic history of the universe, but there are still debates on structural backreactions and the precise form of the vacuum energy.
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