ShahnilaCIIT/FA19-RMT-086/LHRDr. Rabia SaleemLHR TP 74462026-05-052021https://repository.cuilahore.edu.pk/123456789/3821In this thesis, we explore the phenomenon of cosmic evolution using curved FLRW space-time bounded by apparent horizon with a specific holographic cut-off. To this end, we use the framework of Rastall gravity and universe is assumed to be consists of interacting/non-interacting dark energy and dark matter. In both scenarios, we evaluate exact solutions of the dynamical equa- tions and constraint the holographic parameter c2(z), assuming a slowly vary- ing function of red-shift during non-interacting model. For interacting model, we consider c2 as a constant function of red-shift. Moreover, we analyze nature of the obtained results via deceleration parameter (q), statefinder pair (j, s) and Om(z)-diagnostic by constraining the involved model parameters using latest observational data. The graphical analysis showed that interacting model is very close to ΛCDM model as compared to non-interacting case. We conclude that this holographic proposal is enough to describe the cosmic evolution at an accelerating rate.enDepartment of MathematicsFA19MathematicsAccelerating ExpansionFLRW Space-TimeRastall GravityDr. Rabia SaleemThesis