5 M ay 1 99 9 Superconducting cosmic string in Brans - Dicke theory

In the present work, the gravitational field of superconducting cosmic string has been investigated in the context of Brans-Dicke theory of gravity. We have presented two kind of solutions for the spacetime in the far field zone of the string. When the B-D scalar field is switched off, one of the solutions reduces to the solution earlier obtained by Moss and Poletti in General Relativity. 1 Spontaneous symmetry breaking in gauge theories may give rise to some topo-logically trapped regions of a false vacuum namely domain walls, cosmic strings or monopoles depending on the dimension of the region[1]. Amongst these, cosmic strings have gained a lot of attention in recent years as a possible seed for galaxy formation. Strings arising from the breaking of a U(1) local symmetry are called local strings whereas those arising from the breaking of U(1) global symmetry are called the global strings. The gravitational fields of both local and global strings have been investigated by many authors in recent past [2]-[8]. It has been demonstrated by Witten [9] that under certain conditions of local gauge symmtery breaking, cosmic strings might behave as superconductors whose motion through astronomical magnetic fields can produce interesting effects. Peter[10] has emphasized that superconductivity is a rather generic feature of cosmic string models. Massive superconducting strings may have important role to play in the generation of large scale magnetic fields[11, 12]. For the superconducting string, there is a current along the symmtery axis and consequently a magnetic field in the transverse direction. The geometry is no longer boost invariant. Moss and Poletti [13] first investigated the gravitational field of such a string assuming that at large distances from the core of the string, the energy stress tensor is dominated by the magnetic field alone. Later, Demiansky [14] investigated the particle motion in the spacetime given by Moss and Poletti. Scalar tensor theories, especially the Brans-Dicke(BD) theory of gravity [15], which is compatible with the Mach's principle, have been considerably revived in the recent years. It was shown by La and Steinhardt [16] that because of the interaction of the BD scalar field and the higgs type sector, which undergoes a strongly first-order phase transition, the exponential inflation as in the Guth model [17] could be slowed down to power law one. The " graceful exit " in inflation is thus resolved as the phase transition completes via bubble nucleation. On the …