Weak scale from the maximum entropy principle

The theory of the multiverse and wormholes suggests that the parameters of the Standard Model (SM) are fixed in such a way that the radiation of the S-3 universe at the final stage S-rad becomes maximum, which we call the maximum entropy principle. Although it is difficult to confirm this principle generally, for a few parameters of the SM, we can check whether S-rad actually becomes maximum at the observed values. In this paper, we regard S-rad at the final stage as a function of the weak scale (the Higgs expectation value) v(h), and show that it becomes maximum around v(h) = O(300 GeV) when the dimensionless couplings in the SM, i.e., the Higgs self-coupling, the gauge couplings, and the Yukawa couplings are fixed. Roughly speaking, we find that the weak scale is given by v(h) similar to T-BBN(2)/(M-pl y(e)(5)), where y(e) is the Yukawa coupling of electron, T-BBN is the temperature at which the Big Bang nucleosynthesis starts, and M-pl is the Planck mass.