Big bang as a topological quantum phase transition

It has been argued that a particular type of quantum-vacuum variable $q$ can provide a solution to the main cosmological constant problem and possibly also give a cold-dark-matter component. We now show that the same $q$-field may suggest a new interpretation of the big bang, namely as a quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by the equilibrium values $q=\pm q_0$ and there is a kink-type solution $q(t)$ interpolating between $q=-q_0$ for $t\to -\mathrm{\infty }$ and $q=+q_0$ for $t\to \mathrm{\infty }$, with conformal symmetry for $q=0$ at $t=0$.