Einstein’s relativity ideas have not yet exhausted their applications to elucidate the physical realities of the universe and will be demonstrated to have been instrumental in the origin of the cosmic inflationary epoch for which there is still no clear explanation. The biggest problem in cosmology is our current ignorance about what preceded time 0 of our cosmological history. Moreover all published concepts about how a universe or universes could originate are highly speculative and simplistic. For this reason this paper is one of a series dealing with the micro and macro scale realities of the universe which aim to eventually lead to a proper and self-explanatory concept of the origin of our universe right from whatever could have preceded time 0. Pending this new concept we agree with the generally accepted occurrence of the Planck epoch followed by a grand unification epoch up to 10x -36 s to be immediately followed by the inflationary epoch. Minkowski’s reputed space/time statement that space and time being separate entities was doomed could evolve towards the realization that energy, matter, and gravitation might all together constitute an independent integrated reality of its own which encompasses the basis of consciousness in all its expressions. Such an integrated reality, intimately linked to the mechanism which created our universe, could, we are quite confident, help us to eventually understand the scientific basis of what constitutes metaphysics. Anticipating this possibility we show how Einstein relativity is still alive in the new concept, we report here, of the inflationary epoch believed to have occurred sometime at 10x -36 s after the appearance of the initial energy mass which would produce the universe. The initial pure energy, soon after time 0 with c as average velocity, should have an infinitely contracted space-time and would, in the presence of, first, a small fraction of massive hadron particles, inevitably begin inflating cataclysmically and exponentially. The successive formation of another small fraction of leptons like electrons, positrons and others would accentuate this inflation. We show that Einstein’s special relativity theory and the second law of thermodynamics, also called the law of increased entropy, satisfactorily explain the exponential inflationary epoch.