Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-08-31
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, 3 figures; new appendices and references added
Scientific paper
In an earlier paper, it is proposed that, due to resonance tunneling effect, tunneling from a large cosmological constant $\Lambda$ site in the stringy comic landscape can be fast, while tunneling from a small $\Lambda$ site may take exponentially long time. Borrowing the renormalization group analysis of the conductance in the Anderson localization transition, we treat the landscape as a multi-dimensional random potential and find that the vastness of the landscape leads to a sharp transition at a small critical value $\Lambda_{c}$ from fast tunneling for $\Lambda > \Lambda_{c} $ to suppressed tunneling for $\Lambda_{c} > \Lambda >0$. Mobility in the landscape makes eternal inflation highly unlikely. As an illustration, we find that $\Lambda_{c}$ can easily be exponentially small compared to the string/Planck scale. These properties may help us in finding a qualitative understanding why today's dark energy is so small.
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