A Renormalization Group Approach to the Cosmological Constant Problem

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.