Accelerating Expansion of the Universe within Rastall Gravity Via Cosmography of Some Dark Energy Models

Abstract

This thesis is mainly focused to investigate the cosmological implications of Rastall gravity with the help of two dark energy models, i.e., new Tsallis agegraphic dark energy (NTADE) and Sharma-Mittal holographic dark energy (SMHDE) for interacting and non-interacting cases. The background of flat FLRW space-time is being considered to develop the dynamical system of equa- tions. To check the viability of these models and to distinguish between them, we develop important cosmological parameters including equation of state pa- rameter, deceleration parameter, square speed of sound, statefinder and Om(z) diagnostic for both cases. By constraining the involved model parameters, it is observed that equation of state parameter for NTADE model lies in phantom re- gion for both interacting and non-interacting cases. Whereas for non-interacting SMHDE, it shows quintom as well as quintessence regions depending on the values of model parameter δ, and it indicates only the phantom region for inter- acting case. The ωD − ω′ D pair shows freezing and thawing regions for non-interacting NTADE while only freezing region for interacting NTADE and non-interacting SMHDE. For interacting SMHDE case, it shows freezing and thawing regions as well as region transition from freezing to thawing. The statefinder pair (j, s) for NTADE and SMHDE indicates a rich behavior as it shows different DE eras; phantom, quintessence as well as Chaplygin gas for both cases. We conclude that non-interacting SMHDE is more physically viable model than NTADE model because it approaches to ΛCDM limit and also the results for this model lie in stable region as shown by graphical analysis of the square speed of sound