  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.
