Non-Abelian cosmic string in the Starobinsky model of gravity

In this paper, we analyze numerically the behaviour of the solutions corresponding to a non-Abelian cosmic string in the framework of the Starobinsky model, i.e. where $f(R)=R + \zeta R^2$. We perform the calculations for both an asymptotically flat and asymptotically (anti)de Sitter spacetimes. We found that the angular deficit generated by the string decreases as the parameter $\zeta$ increases, in the case of a null cosmological constant. For a positive cosmological constant, we found that the cosmic horizon is affected in a non-trivial way by the parameter $\zeta$.