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Tunneling wave function of the universe II: the backreaction problem
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abstract
The tunneling wave function of the universe is calculated exactly for a de Sitter minisuperspace model with a massless conformally coupled scalar field, both by solving the Wheeler-DeWitt equation and by evaluating the Lorentzian path integral. The same wave function is found in both approaches. The back-reaction of quantum field fluctuations on the scale factor amounts to a constant renormalization of the vacuum energy density. This is in contrast to the recent suggestion of Feldbrugge $et$ $al.$ that the back-reaction should diverge when the scale factor gets small, $a \to 0$. Similar results are found for a massive scalar field in the limit of a large mass. We also verified that the tunneling wave function can be expressed as a transition amplitude from a universe of vanishing size with the scalar field in the state of Euclidean vacuum, as it was suggested in our earlier work.
Forward citations
Cited by 3 Pith papers
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On quantum creation of a toroidal universe
Toroidal universes with vacuum energy are geodesically incomplete, and their semiclassical nucleation instantons are singular, so quantum creation from nothing cannot be described within semiclassical quantum gravity.
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Tunneling wave function of a closed universe is recovered as the ε o0 limit of a Neumann-plus-small-domain path integral with radiation-induced throat, excluding the unsuppressed outer saddle.
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The Wave Function of the Universe and Inflation
Rearranging the Wheeler-DeWitt equation defines the inflaton potential in terms of an arbitrary wave-function phase and amplitude; nothing constrains that wave function, so the potential is relabeled rather than deriv...
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