Lorentzian vacuum transitions: Open or closed universes? Article Swipe
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· 2021
· Open Access
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· DOI: https://doi.org/10.1103/physrevd.104.026013
· OA: W3109289393
We consider the generalisation of quantum tunneling transitions in the WKB\napproximation to the time-independent functional Schr\\"odinger and\nWheeler-DeWitt equations. Following a Lorentzian approach, we compute the\ntransition rates among different scalar field vacua and compare with those\nperformed by Coleman and collaborators using the Euclidean approach. For\ngravity, we develop a general formalism for computing transition rates in\nWheeler's superspace. This is then applied to computing decays in flat space\nand then to transitions in the presence of gravity. In the latter case we point\nout the complexities arising from having non-positive definite kinetic terms\nillustrating them in the simplified context of mini-superspace. This\ncorresponds to a generalisation of the well-known `tunneling from nothing'\nscenarios. While we can obtain the leading term for the transitions obtained by\nEuclidean methods we also point out some differences and ambiguities. We show\nthat there is no obstruction to keeping the spherically ($SO(4)$) symmetric\nclosed slicing for the new vacuum after a de Sitter to de Sitter transition. We\nargue that this is the natural Lorentzian realisation of the Coleman-De Luccia\ninstanton and that a closed universe is also obtained if the mini-superspace\nassumption is relaxed. This is contrary to the open universe predicted by\nColeman-De Luccia which relies on an analytic continuation performed after\nbubble nucleation. Our findings may have important cosmological implications\nrelated to the origin of inflation and to the string landscape. In particular,\nthey question the widespread belief that evidence for a closed universe would\nrule out the string landscape.\n
