The Hybrid Euclidean-Lorentzian Universe: Stability Considerations and the Point of Transition

The limited velocity implied by Lorentzian signature, prevents the universe to reach thermodynamic equilibrium implied by the CMB. Rapid expansion can occur by following Hawking and assuming a primordial Euclidean metric, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. Moreover, a mathematical model was given regarding the development of current Lorentzian spacetime from the early Euclidean space-time in which problems such as initial singularity and the homogeneity of the CMB are solved. However, stability properties of the hybrid model were not discussed yet, nor was a mathematical criterion for the transition between the Euclidean and Lorentzian era’s defined, those will be discussed here to some extent.