A Renormalization Group Approach to the Cosmological Constant Problem

Abstract

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.

25 pages, 3 figures; new appendices and references added

References in corpus (4)

• The Anthropic Landscape of String Theory
• A Wrinkle in Coleman - De Luccia
• Graceful exit from a stringy landscape via MSSM inflation
• The Boundedness of Euclidean Gravity and the Wavefunction of the Universe