In the early stage of the universe, during the hadronic era, the light velocity was larger than c,  in fact was v=75c. This implies that light velocity has been decreasing in time slowly, from v down to the present value c. On the other hand, based on the measurements of 128 quasar absorption lines, the average increase in fine-structure constantαwas6×10^-6 over the past 6~12Ga. Scientists think it was aroused by the light-speed variation. It would be interesting to investigate if these facts have influenced the past history of the universe. This paper also discusses some problems of faster-than-light research profoundly, such as the velocity definition of the microscopic particles, the velocity of gravitation, the interaction speed of the quantum-entangle-state(QES), and the over distance action.