The Third Quantization: To Tunnel or Not to Tunnel?

Within the framework of the third quantization, we consider the possibility that an initially recollapsing baby universe can enter a stage of near de Sitter inflation by tunnelling through a Euclidean wormhole that connects the recollapsing and inflationary geometries. We present the solutions for the evolution of the scale factor in the Lorentzian and Euclidean regions as well as the probability that the baby universe indeed crosses the wormhole when it reaches its maximum size.This article is based upon work from COST Action CA15117 “Cosmology and Astrophysics Network for Theoretical Advances and Training Actions (CANTATA)”, supported by COST (European Cooperation in Science and Technology). The work of M.B.-L. is supported by the Basque Foundation of Science Ikerbasque. She and J.M. also wish to acknowledge the partial support from the Basque government Grant No. IT956-16 (Spain) and FONDOS FEDER under grant FIS2014-57956-P (Spanish government). The research of M.K. was financed by the Polish National Science Center Grant DEC-2012/06/A/ST2/00395 and by a grant for the Short Term Scientific Mission (STSM) “Multiverse impact onto the cosmic microwave background and its relation to modified gravity” (COST-STSM-CA15117-36137) awarded by the above-mentioned COST Action. M.K. and J.M. would like to thank the Centro de Matemática e Aplicações of the Universidade da Beira Interior in Covilhã, Portugal for kind hospitality while part of this work was done. M.K. also thanks M.P. D ˛abrowski for fruitful discussions. J.M. is thankful to UPV/EHU for a PhD fellowshi