Late Time Cosmic Acceleration in Modified Gravity and Gauss-Bonnet Cosmology

This thesis focuses on late-time cosmic acceleration within modified theories of gravity, using various observational data sets and statistical analysis. The Universe is assumed to be spatially homogeneous and isotropic and is described by the Friedmann Lema\ⁱtre Robertson Walker metric. The late-time acceleration of the Universe has posed a significant challenge to contemporary cosmology. General relativity addresses this by introducing the cosmological constant, forming the basis of the standard cosmological model (ΛCDM). However, this model has limitations, leading cosmologists to explore alternative explanations for late-time acceleration. These alternatives range from models involving a dynamic dark fluid known as dark energy, to large-scale modifications of gravitational interaction, known as modified gravity. The formulation of general relativity fundamentally changed our understanding of gravitation, redefining gravity as a manifestation of the curvature of spacetime rather than a force as described by Newton. Despite its success, general relativity has shown incompatibilities with observations, necessitating the introduction of dark matter and dark energy....