  We study the spectral index of curvature perturbations for inflationary
models where the driving scalar field is coupled to a relativistic fluid
through a friction term $\Gamma$. We find that only a very small friction term
- $\Gamma \ll H$, with H being the Hubble parameter during inflation - is
allowed by observations, otherwise curvature fluctuations are generated with a
spectral index $n_s$ unacceptably red. These results are generic with respect
to the inflationary potential and known dependence of the friction term on the
scalar field and the energy density of the relativistic fluid. We compare our
findings with previous investigations.
