The radiational contributions, electromagnetic and gravitational, to energy density in the cosmological equation must be negative. This creates natural turning points for a cyclic cosmological model. The negative pressure of the electromagnetic radiation would prevent the collapse of the universe in a prior contracting phase, while the positive pressure of the gravitational radiation would prevent it from expanding forever. Such a cosmological model avoids the problems of a singular past, and evades an ever-accelerating future. The picture is that of an oscillating universe full of stars, that eternally build and destroy the various forms of matter and life, all in a framework of energy conservation. Assuming that the temperature of microwave radiation is a true measure of the electromagnetic energy density of the universe, and that the supernovae data and redshifts are reliable, we can determine (tentatively) the parameters of our model, with an appropriate Hubble fraction of 0.50, and a deceleration parameter of 0.55, and estimate the time that passed, about 12.8 Gyr, since the initiation of the expansion phase, and the time that remains, about 1066 Gyr, before the return to contraction.