Gravitational transitions via the explicitly broken symmetron screening mechanism

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