Can observations look back to the beginning of inflation?

TL;DR

This paper investigates whether cosmic microwave background observations can reveal conditions from the very start of inflation, concluding that under certain approximations, initial conditions are preserved and observable.

Contribution

It introduces a general solution for correlation functions in an interacting scalar field, showing no loss of memory of initial conditions within a derivative expansion approximation.

Findings

Initial conditions are preserved in the correlation functions under the studied approximation.

Observations can potentially access the initial spectrum at the start of inflation.

No significant loss of memory of initial states occurs in the model.

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.