Supermassive screwed cosmic string in dilaton gravity

Abstract

The early Universe might have undergone phase transitions at energy scales much higher than the one corresponding to the Grand Unified Theories (GUT) scales. At these higher energy scales, the transition at which gravity separated from all other interactions; the so-called Planck era, more massive strings called supermassive cosmic strings, could have been produced, with energy of about 10^{19}GeV. The dynamics of strings formed with this energy scale cannot be described by means of the weak-field approximation, as in the standard procedure for ordinary GUT cosmic strings. As suggested by string theories, at this extreme energies, gravity may be transmitted by some kind of scalar field (usually called the {\it dilaton}) in addition to the tensor field of Einstein's theory of gravity. It is then permissible to tackle the issue regarding the dynamics of supermassive cosmic strings within this framework. With this aim we obtain the gravitational field of a supermassive screwed cosmic string in a scalar-tensor theory of gravity. We show that for the supermassive configuration exact solutions of scalar-tensor screwed cosmic strings can be found in connection with the Bogomol'nyi limit. We show that the generalization of Bogomol'nyi arguments to the Brans-Dicke theory is possible when torsion is present and we obtain an exact solution in this supermassive regime, with the dilaton solution obtained by consistency with internal constraints.