Abstract
We specify the semiclassical no-boundary wave function of the universe without relying on a functional integral of any kind. The wave function is given as a sum of specific saddle points of the dynamical theory that satisfy conditions of regularity on geometry and field and which together yield a time neutral state that is normalizable in an appropriate inner product. This specifies a predictive framework of semiclassical quantum cosmology that is adequate to make probabilistic predictions, which are in agreement with observations in simple models. The use of holography to go beyond the semiclassical approximation is briefly discussed.
Highlights
It is an inescapable inference from the physics of the last century that we live in a quantum mechanical Universe
This specifies the predictive framework of semiclassical quantum cosmology needed to derive probabilistic predictions for features of our observed Universe
In its original form [26], the tunneling wave function was defined in terms of outgoing mode boundary conditions on the Wheeler-DeWitt equation and involved regular noboundary saddle points at the semiclassical level
Summary
The mathematical complexities associated with integrals over quantum spacetimes lead one to suspect there might be a simpler, more direct approach to defining cosmological wave functions in the semiclassical approximation. This is relevant for the comparison of theories of the state of the Universe with observations, which is mostly done in the semiclassical approximation only. II with a discussion of a very simple example: the groundstate wave functional of linearized gravity We show this can be represented by functional integrals in various different ways and from saddle points of an appropriately defined action with no integral at all.
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