Towards a Solution of the Negative Mode Problem in Quantum Tunnelling with Gravity
arXiv:1504.04334 · doi:10.1103/PhysRevD.92.023506
Abstract
In the absence of gravity, one can prove that tunnelling instantons exhibit exactly one negative mode in their spectrum of fluctuations. It is precisely the existence of this tunnelling negative mode that warrants an interpretation of these solutions as mediating the decay of a metastable vacuum. In the presence of gravity the situation is much more subtle, not least because of diffeomorphism invariance. New complications arise here: in particular, the kinetic term of the fluctuations can change sign somewhere along the instanton. We show that in this case the mode functions remain non-singular, and the tunnelling negative mode continues to exist. Moreover, the eigenvalues vary continuously when the potential is varied such that the kinetic term of the fluctuations switches sign. However, the negative kinetic term implies the additional existence of an infinite tower of negative modes, whose significance and interpretation remain elusive.
32 pages, 13 figures, v3: more references added, published version
References in corpus (13)
- Higgs inflation at the critical point
- Higgs inflation still alive
- The lifetime of the electroweak vacuum and sensitivity to Planck scale physics
- Gravitational corrections to Standard Model vacuum decay
- Thermal derivation of the Coleman-De Luccia tunneling prescription
- Top mass determination, Higgs inflation, and vacuum stability
- Cosmological Perturbations Through a Non-Singular Ghost-Condensate/Galileon Bounce
- The Higgs vacuum is unstable
- The number of negative modes of the oscillating bounces
- Fluctuations about Cosmological Instantons
- Negative modes of Coleman-De Luccia bounces
- Creation of wormholes by quantum tunnelling in modified gravity theories
- Recovering the Negative Mode for Type B Coleman-de Luccia Instantons