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Register a new userA Renormalization Group Approach to the Cosmological Constant Problem
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S.-H. Henry Tye
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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 todays dark energy is so small.
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Renormalization group (RG) applications to cosmological problems often encounter difficulties in the interpretation of the field independent term in the effective potential. While this term is constant with respect to field variations, it generally depends on the RG scale k. Since the RG running could be associated with the temporal evolution of the Universe according to the identification $k sim 1/t$, one can treat the field independent constant, i.e., the $Lambda$ term in Einsteins equations as a running (scale-dependent) parameter. Its scale dependence can be described by nonperturbative RG, but it has a serious drawback, namely $k^4$ and $k^2$ terms appear in the RG flow in its high-energy (UV) limit which results in a rampant divergent behaviour. Here, we propose a subtraction method to handle this unphysical UV scaling and provides us a framework to build up a reliable solution to the cosmological constant problem.
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