Abstract
The path integration technique recently developed for the statistical sum of the microcanonical ensemble in cosmology is applied to the calculation of the one-loop preexponential factor in the cosmological model generated by a conformal field theory with a large number of quantum species -- the model of initial conditions possibly related to the resolution of the cosmological constant and landscape problems. The result is obtained for the family of background cosmological instantons with one oscillation of the FRW scale factor. The magnitude of the prefactor is analytically and numerically estimated for fields of various spins conformally coupled to gravity, which justifies the validity of semiclassical expansion for this family of cosmological instantons.
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