The No-Negative Mode Theorem in False Vacuum Decay with Gravity
arXiv:gr-qc/9901082 · doi:10.1016/S0550-3213(99)00369-7
Abstract
The so-called negative mode problem in the path integral approach to the false vacuum decay with the effect of gravity has been an unsolved problem. Several years ago, we proposed a conjecture which is to be proved in order to give a consistent solution to the negative mode problem. We called it the ``no-negative mode conjecture''. In the present paper, we give a proof of this conjecture for rather general models. Recently, we also proposed the ``no-supercritical supercurvature mode conjecture'' that claims the absence of supercritical supercurvature modes in the one-bubble open inflation model. In the same paper, we clarified the equivalence between the ``no-negative mode conjecture'' and the ``no-supercritical supercurvature mode conjecture''. Hence, the latter is also proved at the same time when the former is proved.
14 pages, 8 postscript figures, added references, corrected some typos
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