S. Gratton et N. Turok, Cosmological perturbations from the no boundary Euclidean path integral - art. no. 123507, PHYS REV D, 6012(12), 1999, pp. 3507
We compute, from first principles, the quantum fluctuations about instanton
saddle points of the Euclidean path integral for Einstein gravity coupled
to a scalar held. The Euclidean two-point correlator is analytically contin
ued into the Lorentzian region where it describes the quantum mechanical va
cuum fluctuations in the state described by no boundary proposal initial co
nditions. We concentrate on the density perturbations in open inflationary
universes produced from cosmological instantons, describing the differences
between non-singular Coleman-De Luccia and singular Hawbing-Turok. instant
ons. We show how the Euclidean path integral uniquely specifies the fluctua
tions in both cases. [S0556-2821(99)01022-X].