Circular Loop Equation of a Cosmic String in Gauss--Bonnet--de

We perform the analysis of evolution of cosmic string loops in the background of Gauss--Bonnet--de Sitter. The equation of motion of cosmic string loops in this spacetime is derived. Having solved the equation numerically, we investigate the dependence of the loop evolution on the values of α, related
to the Gauss--Bonnet coupling. In the Gauss--Bonnet--de Sitter spacetimes with different dimensionality there exists a special parameter α_m. In the environment with α>α_m, all the cosmic string loops will collapse to form black holes. Within the region 0<α<α_m, the stronger Gauss--Bonnet effect will lead more cosmic string loops, including smaller ones, to form black holes. The larger the value of α is, the smaller the special values that exist, and only the cosmic string loops with initial radius larger than the special values can expand and evolve instead of becoming black holes.