  A generic feature of inflationary models in supergravity/string constructions
is vacuum misalignment for the moduli fields. The associated production of
moduli particles leads to an epoch in the post-inflationary history in which
the energy density is dominated by cold moduli particles. This modification of
the post-inflationary history implies that the preferred range for the number
of e-foldings between horizon exit of the modes relevant for CMB observations
and the end of inflation $(N_k)$ depends on moduli masses. This in turn implies
that the precision CMB observables $n_s$ and $r$ are sensitive to moduli
masses. We analyse this sensitivity for some representative models of inflation
and find the effect to be highly relevant for confronting inflationary models
with observations.
