Dynamically broken Lorentz invariance from the Higgs sector?

The original Abelian U(1) Higgs model in flat spacetime is enlarged by the addition of one real scalar with a particular potential. It is then shown that, while maintaining the original masses of the vector boson and Higgs scalar, there exists a time-dependent homogeneous solution of the classical field equations, which corresponds to dynamical breaking of Lorentz invariance (DBLI). The same DBLI mechanism holds for the standard model enlarged by the addition of a real isosinglet scalar with an appropriate potential. The resulting DBLI with an assumed TeV energy scale would manifest itself primarily in the interactions of the two scalar particles. In principle, this DBLI could feed into the neutrino sector and give rise to a superluminal maximum velocity.