Anisotropic to Isotropic Phase Transitions in the Early Universe

Abstract

We propose that the early Universe was not Lorentz symmetric and that a gradual transition to the Lorentz symmetric phase occurred. An underlying form of the Dirac equation hints to such a transition for fermions. Fermions were coupled to space-time in a non-trivial manner such that they were massless in the Lorentz violating phase. The partition function is used as a transfer matrix to model this transition on a two level thermodynamics system that describes how such a transition might have occurred. The system that models this transition evolves, with temperature, from a state of large to negligible entropy and this is interpreted as describing the transition to a state with Lorentz symmetry. In addition to this, analogy is created with the properties of this system to describe how the fields were massless and how a baryon asymmetry can be generated in this model.