Kaluza-Klein Universe with Cosmic Strings and Bulk Viscosity in a Scalar-Tensor Theory of Gravitation
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Kaluza-Klein Universe with Cosmic Strings and Bulk Viscosity in a Scalar-Tensor Theory of Gravitation D.R.K. Reddy · R. Santhi Kumar · T.V. Pradeep Kumar
Received: 26 September 2012 / Accepted: 27 November 2012 / Published online: 8 December 2012 © Springer Science+Business Media New York 2012
Abstract A five dimensional Kaluza-Klein space-time is considered in the frame work of a scalar-tensor theory proposed by Saez and Ballester (Phys. Lett. A 113, 467, 1985) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional strings. A barotropic equation of state for the pressure and density is assumed to get a determinate solution of the field equations. Also the bulk viscous pressure is assumed to be proportional to the energy density. The physical and kinematical properties of the model are also discussed. Keywords Kaluze-Klein universe · Scalar-tensor theory · Cosmic string · Bulk viscosity 1 Introduction Several theories of gravitation have been proposed as alternative to Einstein’s theory to incorporate certain desirable features in the original theory. Noteworthy among them are scalar-tensor theories of gravitation [1–8] and Rosen’s [9] bimetric theory of gravitation. Scalar-tensor theories are considered to be very important to describe the gravitational interactions near the Plank’s scale, string theory, extended inflation and many higher order theories that imply scalar field. Brans-Dicke [1] scalar-tensor theory of gravitation introduces an additional scalar field φ besides the metric tensor gij and a dimensionless coupling D.R.K. Reddy () Department of Science and Humanities, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India e-mail: [email protected] R. Santhi Kumar Department of Basic Science and Humanities, Aditya Institute of Technology and Management, Tekkali, Srikakulam, Andhra Pradesh, India e-mail: [email protected] T.V. Pradeep Kumar ANU College of Engg & Tech, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India e-mail: [email protected]
Int J Theor Phys (2013) 52:1214–1220
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constant ω. This theory approaches general relativity for large values of the coupling constant ω. Saez and Ballester [2] formulated a scalar-tensor theory of gravitation in which the metric is coupled with a dimensionless scalar field in a simple manner. This coupling gives a satisfactory description of the weak fields. In spite of the dimensionless character of the weak fields an antigravity regime appears. This theory also suggests a possible way to solve ‘ missing’ matter problem in non-flat FRW cosmologies. During the phase transition in the early universe, spontaneous symmetry breaking gives rise to a random network of stable line like topological defects known as cosmic strings. It is well known that massive strings serve as seeds for the large structures like galaxies and cluster of galaxies in the universe. Several authors [10–32] have investigated the different aspects of string cosmological models either in the framework of general relativ
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