Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by \(f(R) = R - 2\Lambda + \eta R^2 + \rho R^m\), with \(m > 2\). As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters \(\eta \) and \(\rho \) increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant.