Muhammad Waheed ZafarSP19-RMT-011LHR TP 6471Dr. Rabia Saleem2026-03-122021https://repository.cuilahore.edu.pk/handle/123456789/2726The main focus of this thesis is to investigate accelerating expansion of our universe in the framework of Rastall theory of gravity (RTG) using non-linear inhomogeneousequationofstate(EoS)forFriedmann-Robertson-Walker(FRW) model. First we findthesolution of Hubble parameter, energy density and scale factor investigating the transition from non-phantom to phantom era. We study transition towards superaccelerating phase, i.e., the case when third derivative of the scale factor is positive. We find present and future singularity for our model. Second to check the thermodynamical evolution of cosmos, we find the product of temperature and entropy (TdS), and observe it graphically. To check the nature of cosmos, we find some important cosmological parameters using obtained solutions including deceleration, jerk, variable jerk, gradually varying jerk and snap parameters. Through detailed graphical analysis, we found that RTGis a good candidate to represent accelerating cosmic expansion.enDr. Rabia Saleemsp19Department of MathematicsMATHEMATICSCosmic SolutionsRastall GravityThesis