Initial conditions from the action principle: Application to cosmology and to false vacuum bubbles

We study models in which parameters such as the gauge coupling constant and mass are functions of some conserved charge in the universe. We first consider the standard Dirac action but in which the mass and electromagnetic coupling constant are a function of the charge in the universe, and then extend this to scalar fields. For a Dirac field in the flat space formulation, the formalism is not manifestly Lorentz-invariant. However, Lorentz invariance can be restored by performing a phase transformation of the Dirac field. For a scalar field, we identify a new feature whereby the initial conditions for the field are derived from the action. For a Higgs field, the initial conditions require that the universe is in a false vacuum state at a certain time slice, which is quite important for inflation scenarios. We also study false vacuum branes using a similar approach. We discuss the use of spoiling terms that violate gauge invariance to introduce this initial condition.