Can observations look back to the beginning of inflation?

Abstract

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.