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arXiv · 1812.08084

Tunneling wave function of the universe II: the backreaction problem

Alexander Vilenkin·Masaki Yamada
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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.

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Alexander Vilenkin, Masaki Yamada. 2018-12-19. Tunneling wave function of the universe II: the backreaction problem. https://doi.org/10.1103/physrevd.99.066010

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