String Regge trajectory in de Sitter space and implications for inflation

We study the spectrum of semiclassical rotating strings in de Sitter space and its consistency. Even though a naive extrapolation of the linear Regge trajectory on flat space implies a violation of the Higuchi bound (a unitarity bound on the mass of higher-spin particles in de Sitter space), the curved space effects turn out to modify the trajectory to respect the bound. Interestingly, as a consequence of accelerated expansion, there exists a maximum spin for each Regge trajectory, which is helpful to make the spectrum consistent with the Higuchi bound, but at the same time, it could be an obstruction to stringy UV completion based on an infinite higher-spin tower. By pushing further this observation, we demonstrate that the vacuum energy $V$ inflating the universe has to be bounded by the string scale $M_s$ as $V\lesssim M_s^4$, if UV completion is achieved with the leading Regge trajectory of higher spin states up to the 4D Planck scale. Its application to inflation in the early universe implies an upper bound on the tensor-to-scalar ratio, $r\lesssim 0.01\times(M_s/10^{16} \text{GeV})^{4}$, which is within the scope of the near future CMB experiments. We also discuss another possibility that UV completion is achieved by multiple Regge trajectories.