Topological defects in gravitational theories with nonlinear Lagrangians.

Abstract

The gravitational field of monopoles, cosmic strings, and domain walls is studied in the quadratic gravitational theory $R+\ensuremath{\alpha}{R}^{2}$ with $\ensuremath{\alpha}|R|\ensuremath{\ll}1$, and is compared with the result in Einstein's theory. The metric acquires modifications which correspond to a short-range "Newtonian" potential for gauge cosmic strings, gauge monopoles, and domain walls, and to a long-range one for global monopoles and global cosmic strings. In this theory the corrections turn out to be attractive for all the defects. We explain, however, that the sign of these corrections in general depends on the particular higher-order derivative theory and topological defect under consideration. The possible relevance of our results to the study of the evolution of topological defects in the early Universe is pointed out.