  The author has suggested that the knee phenomenon in the cosmic ray energy
spectrum at 3 PeV can be explained as a split between a radiation-dominated
expansion and a matter-dominated expansion of an expanding heat bath. The model
proposed in 1985, in fact, predicted that high energy cosmic rays are emitted
from AGN, massive black holes, in agreement with recent data from the Pierre
Auger Observatory. Similarly, the ankle phenomenon at 3 EeV is shown to be
explained by a split between inflational expansion and ordinary material
expansion of the expanding heat bath, not unlike that in the expansion of the
universe. All the spectral indicies in the respective regions of the energy
spectra agree with the theoretical calculation from the respective expansion
rates.
