New Anisotropic Cosmological Models and Two-Fluid Energy Models

The global structure of space-times satisfying Einstein's ¯eld equations remains an active area of research, more than 80 years after the theory of general relativity was formulated. Space-times that are of physical interest can be separated intotwo main types, (i) ones of isolated system and (ii) ones that model the whole universe. This thesis is about the second type, cosmological models. This study is focused on obtaining exact anisotropic solution for Einstein's field equations (EFEs) as a cosmologically accepted physical models for the universe (at least in the early stages). We have investigated the gravitational e®ects of diferent types of matter i.e. electromagnetic field, bulk viscus °uid, cosmic strings and cos-mological constant as the matter (energy) sources in the energy-momentum tensor of the Einstein's field equations. Also, a new class of exact solutions of Einstein's modified field equations in inhomogeneous space-time for perfect fuid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra's manifold. We have obtained solutions by considering the time dependent displacement field. We have also studied the time varying gravitational constant (G) which has many interesting consequences in astrophysics. G-varying cosmology is consistent with whatsoever cosmological observations available at present. The Newtonian constant of gravitation plays the role of a coupling constant between geometry and matter in the Einstein field equation. The large number hypothesis proposed by Dirac leads to a cosmology when G varies with time. The geometrical and physical behaviors of all models are also discussed. Moreover in my research we have investigated the e®ect of interaction between barotropic °uid and dark energy on the equation of state parameter in FRW space-time by considering a variable deceleration parameter.

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