Topological Defects in Gravitational Theories with Non Linear Lagrangians

TL;DR

This paper investigates how quadratic gravitational theories with small corrections modify the gravitational fields of topological defects like monopoles and cosmic strings, revealing attractive corrections that depend on the defect type.

Contribution

It provides a comparative analysis of topological defect gravitational fields in quadratic gravity versus Einstein's theory, highlighting the nature of corrections and their potential cosmological implications.

Findings

Quadratic gravity introduces short-range and long-range potential modifications.

Corrections are attractive for all studied topological defects.

Sign of corrections varies with the specific higher-order theory and defect type.

Abstract

The gravitational field of monopoles, cosmic strings and domain walls is studied in the quadratic gravitational theory $R+\alpha R^2$ with $\alpha |R|\ll 1$, and is compared with the result in Einstein's theory. The metric aquires 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.