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#### Aspects of the negative mode problem in quantum tunneling with gravity

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1906.07033.pdf

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##### Citation

Bramberger, S., Chitishvili, M., & Lavrelashvili, G. V. (2019). Aspects of the
negative mode problem in quantum tunneling with gravity.* Physical Review D,* *100*(12):
125006. doi:10.1103/PhysRevD.100.125006.

Cite as: https://hdl.handle.net/21.11116/0000-0003-D83A-9

##### Abstract

Some solutions describing vacuum decay exhibit a catastrophic instability.

This, so-called negative mode problem in quantum tunneling with gravity, was

discovered 34 years ago and in spite of the fact that in these years many

different groups worked on this topic, it has still not been resolved. Here, we

briefly summarize the current status of the problem and investigate properties

of the bounces, numerically and analytically for physically interesting

potentials. In the framework of the Hamiltonian approach we show that for

generic polynomial potentials the negative mode problem could arise at energies

much lower than the Planck mass, indicating that the negative mode problem is

not related to physics at the Planck scale. At the same time we find that for a

Higgs like potential, as it appears in the standard model, the problem does not

appear at realistic values of the potential's parameters but only at the Planck

scale.

This, so-called negative mode problem in quantum tunneling with gravity, was

discovered 34 years ago and in spite of the fact that in these years many

different groups worked on this topic, it has still not been resolved. Here, we

briefly summarize the current status of the problem and investigate properties

of the bounces, numerically and analytically for physically interesting

potentials. In the framework of the Hamiltonian approach we show that for

generic polynomial potentials the negative mode problem could arise at energies

much lower than the Planck mass, indicating that the negative mode problem is

not related to physics at the Planck scale. At the same time we find that for a

Higgs like potential, as it appears in the standard model, the problem does not

appear at realistic values of the potential's parameters but only at the Planck

scale.