This article provides a physical solution to cosmic inflation, the onset of the radiation epoch and the reheating epoch. It does not require dark energy thanks to a zero cosmological constant. Cosmological inflation is a mathematical solution considered necessary for the coherence of cosmological models. There are several versions of it, but there is currently no physical basis to explain it. We show that the existence of negative heavy masses (but always positive inert masses) makes it possible to explain it and also makes it possible to justify many other phenomena. Experiments are underway to test the hypothesis of negative heavy masses. The first results should be obtained within 1 or 2 years. In this solution, inflation occurs at the onset of the gravitational interaction much earlier than in the commonly accepted chronology. Gravitation gives rise to a negative pressure primordial fluid verifying the inflation conditions known as “slow roll”. It leads to regularity in matter density and temperature of the CMB. The structures of filaments, walls and large cosmic voids (and even superclusters) can be explained as a consequence of the influence of this matter of negative gravitational mass.