Zoya Khan,FA17-RMT-055Contributor(s): Dr. Shamaila Rani, Assistant Profesor [Supervisor]LHR TP 56762026-04-212019https://repository.cuilahore.edu.pk/123456789/3644In this thesis, we examine the thermodynamical behavior of homogeneous and isotropic universe (flat and non-flat) in the framework of f(R,Tφ) grav ity, where R stands for Ricci scalar and Tφ represents the trace of the energy-momentum tensor of a scalar field φ. Throughout we follow the irst-order formalism, that specifies the scalar field to the Hubble parame ter which becomes H = W(φ). By using Bekenstein-Hawking entropy, we analyze the validity of the generalized second law of thermodynamics at ap parent horizon for three different models of W(φ) and discuss the thermal equilibrium condition for these cases as well. We observe that, this gener alized law gives better results only for one model and as well as thermal equilibrium condition satisfies for each value of W(φ) at apparent horizon with Bekenstein-Hawking entropy. Also, we investigate the generalized second law of thermodynamics and thermal equilibrium condition in multi-component scalar field for flat Friedmann Robertson-Walker universe. We are following the first-order formalism and we choose three superpotential models of the Hubble parameter, and by using these models we observe the validity of the generalized law as well as thermal equilibrium condition for Bekenstein entropy. Also, we take three different entropies which are logarithmic corrected, Sharma-Mittal and R´enyi entropies, for each model of W(φi), we study the behavior of the generalized law and thermal equilibrium condition, using all entropies at Hubble horizon. We inspect that, the generalized law is valid and thermal equilibrium condition satisfies only for some casesendepartment of mathematicsLHR TP 5676Fa17examine the thermodynamical behavior of homogeneous and isotropic universe (flat and non-flat) in the framework of f(RTφ) grav itywhere R stands for Ricci scalar and Tφ represents the trace of theThesis