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Abstract

The usual description of inflationary fluctuations uses the framework of
quantum field theory (QFT) in curved spacetime, in which quantum fluctuations
are superimposed on a classical background spacetime. Even for large
fluctuations, such as those envisioned during a regime of eternal inflation,
this framework is frequently used. In the present work we go one step beyond
this description by quantising both the scalar field and the scale factor of
the universe. Employing the Lorentzian path integral formulation of
semi-classical gravity we restrict to a simplified minisuperspace setting by
considering homogeneous transitions. This approach allows us to determine the
dominant geometry and inflaton evolution contributing to such amplitudes. We
find that for precisely specified initial scale factor and inflaton values (and
uncertain momenta), two distinct saddle point geometries contribute to the
amplitude, leading to interference effects. However, when the momenta of both
scale factor and inflaton are specified with sufficient certainty, only a
single saddle point is relevant and QFT in curved spacetime is applicable. In
particular we find that for inflaton transitions up the potential, meaningful
results are only obtained when the initial uncertainty in the inflaton value is
large enough, allowing the dominant evolution to be a complexified slow-roll
solution \emph{down} from a comparatively unlikely position higher up in the
potential.