Abelian cosmic string in the Starobinsky model of gravity

In this paper, I analyze numerically the behaviour of the solutions corresponding to an Abelian string in the framework of the Starobinsky model. The role played by the quadratic term in the Lagrangian density $f(R) = R + \eta R^2$ of this model is emphasized and the results are compared with the corresponding ones obtained in the framework of Einstein's theory of gravity. I have found that the angular deficit generated by the string is lowered as the $\eta$ parameter increases, allowing a well-behaved spacetime for a large range of values of the symmetry-breaking scale.