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Article overview
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Monodromies and functional determinants in the CFT driven quantum cosmology | | A. O. Barvinsky
; D. V. Nesterov
; | | Date: |
18 Nov 2011 | | Abstract: | We apply the monodromy method for the calculation of the functional
determinant of a special second order differential operator
$F=-d^2/d au^2+{ddot g}/g$, $ddot g= d^2g/d au^2$, subject to periodic
boundary conditions with a periodic zero mode $g=g( au)$. This operator arises
in applications of the early Universe theory and, in particular, determines the
one-loop statistical sum for the microcanonical ensemble in cosmology generated
by a conformal field theory (CFT). This ensemble realizes the concept of
cosmological initial conditions by generalizing the notion of the no-boundary
wavefunction of the Universe to the level of a special quasi-thermal state
which is dominated by instantons with an oscillating scale factor of their
Euclidean Friedmann-Robertson-Walker metric. These oscillations result in the
multi-node nature of the zero mode $g( au)$ of $F$, which is gauged out from
its reduced functional determinant by the method of the Faddeev-Popov gauge
fixing procedure. The calculation is done for a general case of multiple nodes
(roots) within the period range of the Euclidean time $ au$, thus generalizing
the previously known result for the single-node case of one oscillation of the
cosmological scale factor. The functional determinant of $F$ expresses in terms
of the monodromy of its basis function, which is obtained in quadratures as a
sum of contributions of time segments connecting neighboring pairs of the zero
mode roots within the period range. | | Source: | arXiv, 1111.4474 | | Services: | Forum | Review | PDF | Favorites | |
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