Bianchi Types II, VIII, and IX String Cosmological Models in Brans-Dicke Theory of Gravitation

V U M Rao,M Vijaya Santhi

doi:10.5402/2012/573967

Abstract

Bianchi types II, VIII, and IX string cosmological models are obtained and presented in a scalar-tensor theory of gravitation proposed by Brans and Dicke (1961) for λ+ρ=0. We also established the existence of only Bianchi type IX vacuum cosmological model for λ=ρ, where λ and ρ are tension density and energy density of strings, respectively. Some physical and geometrical features of the models are also discussed.

Highlights

Brans and Dicke 1 introduced a scalar-tensor theory of gravitation involving a scalar function in addition to the familiar general relativistic metric tensor. In this theory the scalar field has the dimension of inverse of the gravitational constant, and its role is confined to its effects on gravitational field equations
Several aspects of Brans-Dicke cosmology have been extensively investigated by many authors
In this paper we will discuss Bianchi types II, VIII, and IX string cosmological models in a scalar-tensor theory proposed by Brans and Dicke 1

Summary

Introduction

Brans and Dicke 1 introduced a scalar-tensor theory of gravitation involving a scalar function in addition to the familiar general relativistic metric tensor. In this theory the scalar field has the dimension of inverse of the gravitational constant, and its role is confined to its effects on gravitational field equations. − φ−1 φi;j − gij φ;k,k , 1.1 φ;k,k 8π 3 2ω −1T, where Gij Rij − 1/2 Rgij is an Einstein tensor, Tij is the stress energy tensor of the matter, and ω is the dimensionless constant

The equation of motion

Metric and Energy Momentum Tensor

Physical and Geometrical Properties

Conclusions