The path integral for the statistical sum of the microcanonical ensemble in cosmology
arXiv:1012.1568 · doi:10.1088/1475-7516/2011/04/034
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.
LaTex, 22 pages, the discussion of the second zero mode of the dynamical operator is included, references to the path integration method in quantum cosmology are added and typos are corrected
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- Statistical sum in the CFT driven cosmology
- On the functional determinant of a special operator with a zero mode in cosmology
- Monodromies and functional determinants in the CFT driven quantum cosmology