Hawking-Moss transition with a black hole seed
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Springer
Received: July 30, 2020 Accepted: August 25, 2020 Published: September 21, 2020
Ruth Gregory,a,b,c Ian G. Moss,d Naritaka Oshitac and Sam Patricka a
Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, U.K. b Institute for Particle Physics Phenomenology, Department of Physics, Durham University, South Road, Durham DH1 3LE, U.K. c Perimeter Institute, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada d School of Mathematics, Statistics and Physics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, U.K.
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We extend the concept of Hawking-Moss, or up-tunnelling, transitions in the early universe to include black hole seeds. The black hole greatly enhances the decay amplitude, however, order to have physically consistent results, we need to impose a new condition (automatically satisfied for the original Hawking-Moss instanton) that the cosmological horizon area should not increase during tunnelling. We motivate this conjecture physically in two ways. First, we look at the energetics of the process, using the formalism of extended black hole thermodynamics; secondly, we extend the stochastic inflationary formalism to include primordial black holes. Both of these methods give a physical substantiation of our conjecture. Keywords: Black Holes, Solitons Monopoles and Instantons, Models of Quantum Gravity ArXiv ePrint: 2007.11428
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)135
JHEP09(2020)135
Hawking-Moss transition with a black hole seed
Contents 1
2 Hawking-Moss instanton with a black hole seed
3
3 Thermodynamics of the Hawking-Moss process
7
4 Stochastic tunnelling in the presence of a black hole
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5 Conclusion
1
10
Introduction
It is inevitable that quantum processes played an important role in the very earliest stages of our universe. Possibly the most remarkable process of all is the decay of the quantum vacuum state. This is because the change in vacuum state can change the curvature of spacetime, and then vacuum decay becomes a fully non-perturbative quantum gravitational phenomenon. If we can provide a plausible understanding of vacuum decay in this context, then we may learn a little about quantum gravity. Some time ago [1], Hawking and Moss noticed that the simple picture of vacuum decay in a system with a scalar field coupled to gravity produces strange results when the field has a very flat potential. The usual picture of a bubble of true vacuum nucleating inside false vacuum with a distinct bubble wall [2] no longer holds: as the potential becomes flatter, the bubble wall becomes thicker, and the field on either side of the wall becomes closer to either side of the maximum of the potential barrier, until the solution interpolating between each side of the potential maximum can no longer exist. Instead, it appears that the field ‘jumps’ to the top of the
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