In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing, and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions, and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our Universe: $10^{139}\mathrm{years}$. With 95% confidence, we expect our Universe to last more than $10^{58}\mathrm{years}$. The uncertainty is part experimental uncertainty on the top quark mass and on ${\alpha }_s$ and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the $m_t/m_h$ and the $m_t/{\alpha }_s$ planes, with uncertainty bands. To rule out absolute stability to $3\sigma$ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on ${\alpha }_s(m_Z)$ pushed below 0.00025.

• Received 31 August 2017

DOI:https://doi.org/10.1103/PhysRevD.97.056006

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society