Hafiz Haseeb NawazSP22-RMT-005Dr. Shamaila RaniLHR TP 87132026-03-132023-03-13https://repository.cuilahore.edu.pk/handle/123456789/2812In this manuscript, we consider the newly proposed modified theory in which topological invariant Gauss-Bonnet G is coupled with the energy momentum squared (τ 2 = τµντ µν). For this matter-geometric coupling, we consider f(G, τ 2 ) = f(G) + g(τ 2 ) model for flat FRW universe. The dy namics of bouncing cosmology are thoroughly examined within the frame work of underlying viable model,can overcome the singularity’s challenge in standard Big-Bang cosmology. We study power law scale factor and some cosmological bouncing scale factors such as the four types of bounces are matter, oscillatory, super, and symmetric.In this scenario,the equation of state parameter is computed ω and the squared sound speed parameter. We also check the dynamics of ω −ω 0 plane for underlying framework. Interest ingly, it should be noted that every outcome favor the recent observational data.enDepartment of MathematicsMathematicsSP22CosmologicalConsequencesEinsteinCondensateModified GravityThesis