The path integral for the statistical sum of the microcanonical ensemble in cosmology

TL;DR

This paper computes the path integral for the microcanonical ensemble in quantum cosmology, providing a systematic gauge-fixed approach in minisuperspace models with implications for cosmological initial conditions.

Contribution

It presents the first systematic calculation of the Faddeev-Popov path integral in quantum cosmology's minisuperspace sector, incorporating advanced gauge fixing and quantization techniques.

Findings

Successfully calculates the one-loop statistical sum for specific instantons.

Handles residual symmetries using Batalin-Vilkovisky quantization.

Provides a framework for initial condition models based on conformal field theory.

Abstract

The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric. This represents the first example of a systematic calculation of the Faddeev-Popov gauge-fixed path integral in the minisuperspace sector of quantum cosmology. The gauge fixing procedure, together with gauging out local diffeomorphisms, also handles the residual symmetries associated with the conformal Killing vector of the FRW metric and incorporates the Batalin-Vilkovisky quantization technique for gauge theories with linearly dependent generators. For a subset of saddle-point instantons, characterized by a single oscillation of the FRW scale factor, this technique is designed to obtain the one-loop statistical sum in the recently suggested model of cosmological initial conditions generated by a conformal field theory with a large number of quantum species.