The authors provide a mathematically well-defined and detailed study of the Lorentzian path integral for quantum gravity in the semiclassical expansion. The findings show a problematic instability is implied by a basic assumption which is the basis of such fundamental aspects as the stability of quantum de Sitter spacetime, the adiabatic vacuum from which inflation is supposed to start, and a smooth semi-classical beginning of the universe, though addition of radiation might remedy some aspects.
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Feldbrugge et al. (2018) studied this question.
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