On the functional determinant of a special operator with a zero mode in cosmology

The functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in pa...

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Bibliographic Details
Published inJournal of cosmology and astroparticle physics Vol. 2011; no. 4; p. 035
Main Authors Barvinsky, A.O, A.Yu.Kamenshchik
Format Journal Article
LanguageEnglish
Published United States IOP Publishing 01.04.2011
Subjects
ASTROPHYSICS, COSMOLOGY AND ASTRONOMY
BOUNDARY CONDITIONS
CONFORMAL INVARIANCE
COSMOLOGICAL MODELS
COSMOLOGY
EUCLIDEAN SPACE
INSTANTONS
METRICS
OSCILLATIONS
PERIODICITY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
UNIVERSE
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ISSN1475-7516
1475-7516
DOI10.1088/1475-7516/2011/04/035

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Summary:The functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in particular, determines the one-loop statistical sum in quantum cosmology generated by a conformal field theory (CFT). The calculation is done for a special case of a periodic zero mode of this operator having two roots (nodes) within the period range, which corresponds to the class of cosmological instantons in the CFT driven cosmology with one oscillation of the cosmological scale factor of its Euclidean Friedmann-Robertson-Walker metric.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2011/04/035