Gravitational transitions via the explicitly broken symmetron screening mechanism

We generalize the symmetron screening mechanism by allowing for an explicit symmetry breaking of the symmetron $\phi^4$ potential. A coupling to matter of the form $A(\phi)=1+\frac{\phi^2}{M^2}$ leads to an explicitly broken symmetry with effective potential $V_{eff}(\phi)=-\mu^2 (1-\frac{\rho}{\mu^2 M^2})\phi^2 +\frac{\lambda}{2}\phi^4 + 2 \varepsilon \phi^3+\frac{\lambda}{2}\eta^4$. Due to the explicit symmetry breaking induced by the cubic term we call this field the 'asymmetron'. For large matter density $\rho>\rho_*\equiv \mu^2M^2+\frac{9}{4}\varepsilon\eta M^2$ the effective potential has a single minimum at $\phi=0$ leading to restoration of General Relativity as in the usual symmetron screening mechanism. For low matter density however, there is a false vacuum and a single true vacuum due to the explicit symmetry breaking. This is expected to lead to an unstable network of domain walls with slightly different value of the gravitational constant $G$ on each side of the wall. This network would be in constant interaction with matter overdensities and would lead to interesting observational signatures which could be detected as gravitational and expansion rate transitions in redshift space. Such a gravitational transition has been recently proposed for the resolution of the Hubble tension.