  The cosmic microwave background can measure the inflaton potential only if
inflation lasts sufficiently long before the time of horizon crossing of
observable fluctuations, such that non-linear effects in the time evolution of
Green's functions lead to a loss of memory of initial conditions for the
ultraviolet tail of the spectrum. Within a derivative expansion of the quantum
effective action for an interacting scalar field we discuss the most general
solution for the correlation function, including arbitrary pure and mixed
quantum states. In this approximation no loss of memory occurs - cosmic
microwave observations see the initial spectrum at the beginning of inflation,
processed only mildly by the scale-violating effects at horizon crossing
induced by the inflaton potential.
