w = 1/3 to w = −1 evolution in a Robertson–Walker space-time with constant scalar curvature

The Ricci tensor of a Robertson–Walker (RW) space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein’s equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space fixes the limit values w = 1/3 and w = −1, without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition. For this reason, we investigate the ‘toy-universe’ with Hubble parameter h = 0.673 and temperature TCMB = 2.72 K. The model predicts an age of the universe in the range 7.3–13.7 Gyr.