The solution of three new interesting studies, a rotating anisotropic twofluid universe coupled with radiation and a scalar field, are studied here, where the anisotropic pressure is generated by the presence of two non-interacting perfect fluids which are in relative motion with respect to each other. In this problem, special discussion is made of the physically interesting class of models in which one fluid is a perfect comoving radiative fluid which is taken to model the cosmic microwave background and the second a perfect non-comoving fluid which will model the observed material content of the universe. Studying the different aspects of these model universes, the role of the radiation and scalar fields in defining the physical and dynamical properties of these models is specifically discussed. Analysis of the rotational perturbations is also made, in the course of which the amount of anisotropy induced in the pressure distribution by a small deviation from the Friedmann metric is also investigated, and it is observed that such anisotropies could grow faster than the expansion of the universe. All the models obtained in this problem are found to be theoretically satisfactory and thereby substantiate the possibilities of the existence of such astrophysical objects in this universe.

The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied. Unified descriptions of the early evolution of the universe consisting of different phases are investigated. The different properties of the cosmological solutions are discussed and the physical behaviour of the model universes during the radiation-dominated era and also during the big bang scenario are studied. Here we obtain models which are geometrically closed and are thereby ever expanding and evolve from rest from a non-singular hot origin with maximum (finite) energy density and temperature and a small minimum (non-zero) gravitational coupling G