Variation of the fine structureconstant with the scalar field on the cosmological scale

In this thesis, the variation of the fine structure constant on a cosmological time scale was investigated. Firstly, by learning differential calculus techniques, Einstein's theory of gravity was expressed in differential forms. Then, in order to look at the fine structure constant in this theory, an electromagnetic field was added to it. Additionally, a scalar field theory that allows for the variation of this fine structure constant was added in a non-minimal way. To investigate the variation of the fine structure constant on a cosmological scale in the model, solutions were considered under the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. These solutions reveal how the scalar field changes during the radiation-dominated and matter-dominated eras of the universe, and thus how the fine structure constant changes on the cosmological scale. KEYWORDS: Fine Structure Constant, Einstein-Maxwell Theory, Scalar Field, Cosmological Solutions.