Abstract
In this paper we investigate the non-Abelian cosmic string in de Sitter and anti--de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also of the metric tensor for specific values of the physical parameters of the theory. For the de Sitter case, we find the appearance of an horizon. This horizon is consequence of the presence of the cosmological constant, and its position strongly depends on the value of the gravitational coupling. In the anti--de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (00) and $(zz)$ components of the metric tensor. They present a strong increasing behavior for large distance from the string.
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