Circular loop equation of a cosmic string in Gauss-Bonnet-de Sitter spacetimes

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 alpha, related to the Gauss Bonnet coupling. In the Gauss-Bonnet-de Sitter spacetimes with different dimensionality there exists a special parameter alpha(m). In the environment with alpha > alpha(m), all the cosmic string loops will collapse to form black holes. Within the region 0 < alpha < alpha(m), the stronger Gauss-Bonnet effect will lead more cosmic string loops, including smaller ones, to form black holes. The larger the value of alpha 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.