On the functional determinant of a special operator with a zero mode in cosmology
Abstract
The functional determinant of a special second order quantummechanical operator is calculated with its zero mode gauged out by the method of the FaddeevPopov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in particular, determines the oneloop 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 FriedmannRobertsonWalker metric.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 April 2011
 DOI:
 10.1088/14757516/2011/04/035
 arXiv:
 arXiv:1012.1571
 Bibcode:
 2011JCAP...04..035B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 LaTex, 15 pages, a new section is added, containing the discussion of a special case of the operator having the second zero mode, typos are corrected