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Spiky strings in de Sitter space

We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.