String Regge trajectory on de Sitter space and implications to inflation
  We study the spectrum of semiclassical rotating strings on 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, there exists a maximum spin for each Regge trajectory as a
consequence of accelerated expansion, 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 by the leading Regge trajectory
with higher spin states up to the 4D Planck scale. Its application to inflation
at 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.
