Abstract: 

The vacuum states of QCD generically break CP symmetry, and are parameterised by the ‘QCD theta’ variable. The strong CP problem arises because experiment shows that the amount of QCD CP violation must be exceedingly small, at odds with our generic expectation. This problem has a dynamical solution – the QCD axion –  which zeroes any observable effects of CP violation through a relaxation mechanism. 

The vacuum states of electromagnetism and gravity generically break Lorentz symmetry, and are parameterised by a ‘shadow’ charge and matter density. Similar to the case of theta-vacua, we should expect that we live in a generic state of these gauge theories, and would thus observe ‘shadow’ fluids in the universe. Because these fluids can behave like cold dark matter, we could view dark matter’s existence as a confirmation of our expectations about the vacuum of EM and GR. On the other hand, there is a well-known relaxation mechanism – inflation – that, if realised in our universe, would dynamically ruin this solution to the DM problem by diluting the shadow fluids away. Thus one is led to a topsy-turvy version of the strong CP problem – one has to address how not to dynamically relax a generic vacuum state. 

Along the way, I will point out that the Hamiltonian formalism makes clear that 1) symmetry-based approaches to the strong CP problem do not solve it, and 2) choosing generic vacuum states in GR (that do not satisfy the Wheeler-DeWitt equation) offers an extremely simple solution to the ‘problem of time evolution’.