  We compute the universal generic corrections to the power spectrum in
slow-roll inflation due to unknown high-energy physics. We arrive at this
result via a careful integrating out of massive fields in the "in-in" formalism
yielding a consistent and predictive low-energy effective description in
time-dependent backgrounds. The density power spectrum is universally modified
at leading order in $H/M$, the ratio of the scale of inflation to the scale of
new physics; the tensor power spectrum receives only subleading corrections. In
doing so, we show how to make sense of a physical momentum-cut-off in loop
integrals despite dynamical redshifts, and how the result can be captured in a
combined effective action/effective density matrix, where the latter contains
non-adiabatic terms which modify the boundary conditions.
