A possible solution to the strong CP problem

We point out that the long-standing strong CP problem may be resolved by an anthropic argument. The key ideas are: (i) to allow explicit breaking(s) of the Peccei-Quinn symmetry which reduces the strong CP problem to the cosmological constant problem, and (ii) to conjecture that the probability distribution of the vacuum energy has a mild pressure towards higher values. The cosmological problems of the (s)axion with a large Peccei-Quinn scale are absent in our mechanism, since the axion acquires a large mass from the explicit breaking.