  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.
