Large Blue Spectral Isocurvature Spectral Index Signals Time-Dependent
  Mass
  We show that if a spectator linear isocurvature dark matter field degree of
freedom has a constant mass through its entire evolution history, the maximum
measurable isocurvature spectral index that is consistent with the current
tensor-to-scalar ratio bound is about 2.4, even if experiments can be sensitive
to a $10^{-6}$ contamination of the predominantly adiabatic power spectrum with
an isocurvature power spectrum at the shortest observable length scales. Hence,
any foreseeable future measurement of a blue isocurvature spectral index larger
than about 2.4 may provide nontrivial evidence for dynamical degrees of freedom
with time-dependent masses during inflation. The bound is not sensitive to the
details of the reheating scenario and can be made mildly smaller if the
tensor-to-scalar ratio is better constrained in the future.
