Initial condition from the action principle and its application to cosmology and to false vacuum bubbles

TL;DR

This paper explores how initial conditions derived from the action principle influence cosmology and false vacuum bubbles, focusing on models where fundamental constants depend on conserved charges, with implications for inflation and brane scenarios.

Contribution

It introduces a novel approach where initial conditions for scalar fields, including the Higgs, are derived from the action, impacting inflation and false vacuum models.

Findings

Initial conditions for scalar fields are derived from the action.

The universe must be at a false vacuum state at a specific time.

The approach applies to false vacuum branes and involves gauge symmetry considerations.

Abstract

We study models where the gauge coupling constants, masses, etc are functions of some conserved charge in the universe. We first consider the standard Dirac action, but where the mass and the electromagnetic coupling constant are a function of the charge in the universe and afterwards extend this scalar fields. For 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. In the case where scalar field are considered, there is the new feature that an initial condition for the scalar field is derived from the action. In the case of the Higgs field, the initial condition require, that the universe be at the false vacuum state at a certain time slice, which is quite important for inflation scenarios. Also false vacuum branes will be studied in a similar approach. We discuss also the use of "spoiling terms", that violate gauge invariant to introduce these initial condition.