Abstract
The path integral is calculated for the statistical sum of themicrocanonical ensemble in a generic time-parametrization invariantgravitational model with the Friedman-Robertson-Walker (FRW) metric.This represents the first example of a systematic calculation of theFaddeev-Popov gauge-fixed path integral in the minisuperspace sectorof quantum cosmology. The gauge fixing procedure, together withgauging out local diffeomorphisms, also handles the residualsymmetries associated with the conformal Killing vector of the FRWmetric and incorporates the Batalin-Vilkovisky quantizationtechnique for gauge theories with linearly dependent generators. Fora subset of saddle-point instantons, characterized by a singleoscillation of the FRW scale factor, this technique is designed toobtain the one-loop statistical sum in the recently suggested modelof cosmological initial conditions generated by a conformal fieldtheory with a large number of quantum species.
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