1202.3668 (Muhammad Adeel Ajaib)

Anisotropic to Isotropic Phase Transitions in the Early Universe    [PDF]

Muhammad Adeel Ajaib

We attempt to develop a minimal formalism to describe an anisotropic to isotropic transition in the early Universe. Assuming an underlying theory that violates Lorentz invariance, we start with a Dirac like equation, involving four massless fields, and which does not exhibit Lorentz invariance. We then perform transformations that restore it to its covariant form along with a mass term for the fermion field. It is proposed that these transformations can be visualized as waves traveling in an anisotropic media. The transformation $it/ \hbar \rightarrow \beta$ is then utilized to transit to a statistical thermodynamics system and the partition function then gives a better insight into the character of this transition. The statistical system hence realized is a two level system with each state doubly degenerate. We propose that modeling the transition this way can help explain matter antimatter asymmetry of the Universe.

View original: http://arxiv.org/abs/1202.3668