  In a previous paper we have shown that superluminal particles are allowed by
the general relativistic theory of gravity provided that the metric is locally
Euclidean. Here we calculate the probability density function of a canonical
ensemble of superluminal particles as function of temperature. This is done for
both space-times invariant under Lorentz symmetry group, and for space times
invariant under an Euclidean symmetry group. Although only the Lorentzian
metric is stable for normal matter density, an Euclidian metric can be created
under special gravitational circumstances and persist in a limited region of
space-time consisting of the very early universe which is characterized by
extremely high densities and temperatures. Superluminal particles also allow
attaining thermodynamic equilibrium at a shorter duration and also suggest a
rapid expansion of the matter density, thus making mechanism such as inflation
(which demands invoking and ad-hoc scalar field) redundant. This is in
accordance with Occam's razor.
