The Bianchi type-IX cosmological model with variable ω has been studied in the scalar tensor theory of gravitation proposed by Saez and Ballester [Phys. Lett. A 113: 467, 1985] in the presence and absence of magnetic field of energy density ρ b. A special law of variation of Hubble's parameter proposed by Berman [Nuovo Cimento 74 B, 182, 1983] has been used to solve the field equations. The physical and kinematical properties of the model are also discussed.

The new Bianchi type-IX cosmological models with binary mixture of perfect fluid and anisotropic dark energy have been studied. The unique solution of field equations is obtained by assuming that the energy conservation equation of the perfect fluid and dark energy vanishes separately together with a special law for the mean Hubble parameter (Berman, 1983) which yields a constant value of the deceleration parameter and generates two types of solutions, one is of power law type and other is of the exponential type. To have a general description of an anisotropic dark energy component in terms of its equation of state) (de  , a skewness parameters  have been introduced. The statefinder diagnostic pair (i.e.   s r, parameter) is used to characterize different phases of the universe. The various geometric and kinematic properties of the model and the behavior of the anisotropy of the dark energy have been discussed.

Bianchi type-IX cosmological models with variable equation of state (EoS) parameter have been investigated in general relativity when universe is filled with dark energy. The field equations have been solved by considering (i) q B = (variable); (ii) q kt m 1 = − + − , where k and m are constants; (iii) 2 1 = − +. This renders early decelerating and late time accelerating cosmological models. The physical and geometrical properties of the models are also discussed.

An expression is derived where the mass is connected to an integral over the pressure of gravitating matter in the frame work of five dimensional (5D) space time. Keywords: String theory, Kaluza-Klein IntroductionIn view of recent developments in superstring theroy and ten dimensional N = 1 Yang-Mills supergravity in its field theory limit, need higher dimensional space time is incerasing. For this reason, in the recent years there has been considerable interest in theories with higher dimensinal space-times in which extra dimesions are contracted to a very small size, apparently beyond our ability for measurment. Marciano (1984) has pointed out that the experimental detections of time variation of fundamental constants should be strong evidence for the existence of extra dimensions. Since the world around us is manifestly 4D in the present era, both in supersymmetry and Kaluza-Klein ( K K ) theories we need to understand the mechanisms of reduction in size of the extra dimensions in order to realise the 4D world. Kaluza-Klein theories are interesting approaches to unify gravity and guage fields, while supersymmetry and supergravity give a natural unification of matter and force. Wesson (1983, 84) and Reddy (1999) have studied several aspects of five dimensional space-time in variable mass theroy and bimetric theory of relativity respectively. Due to the virial theorem we have the following connection between kinetic and potential energies of an isolated gravitating systemThe potential energy of a static celestial body can be given using Newton's law of gravitation by,

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