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Schlagwörter:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Zusammenfassung:
Recent works have suggested that the no-boundary proposal should be defined
as a sum over regular, not necessarily compact, metrics. We show that such a
prescription can be implemented in the presence of a scalar field. For
concreteness, we consider the model of Garay et al., in which the potential is
a sum of exponentials, and which lends itself to an analytical treatment.
Compared to the earlier implementation, we find that saddle points with
unstable fluctuations can be eliminated by imposition of an appropriate
regularity condition. This leads to the appearance of additional saddle points,
corresponding to unclosed geometries. We argue that such saddles will occur
generically, though we also find in our example that they are subdominant to
the closed, Hartle-Hawking, saddle points. When the potential is positive,
classical spacetime is only predicted for inflationary histories. When the
potential is negative, we recover the AdS gravitational path integral, with a
stable scalar field included. One puzzle that we find is that in general the
path integral must be restricted to sum only over specific, discrete and late
time dependent initial values of the scalar field. Only when the scalar is
required to take real values is this puzzle eliminated, a situation that
moreover leads to advantageous phenomenological characteristics.
