Non-Abelian cosmic string in the Starobinsky model of gravity

TL;DR

This paper numerically investigates non-Abelian cosmic strings within the Starobinsky gravity model, revealing how the string's angular deficit and cosmic horizon are influenced by the model's parameters in different spacetime backgrounds.

Contribution

It provides the first numerical analysis of non-Abelian cosmic strings in the Starobinsky model of gravity, exploring effects on spacetime geometry.

Findings

Angular deficit decreases with increasing  in flat spacetime.

Cosmological horizon behavior is non-trivial with positive cosmological constant.

Results differ between asymptotically flat and (anti)de Sitter spacetimes.

Abstract

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 $\zeta$.