We discuss the implications of the Calogero hypothesis on the "cosmic origi
n of quantization",(1) and of the variation of h with time it implies, for
cosmology. We focus on two issues: (a) how the relation between redshift an
d distance would be modified; and (b) how the observations on the cosmic ba
ckground radiation, and the estimation they give of the time elapsed since
its production, would be interpreted in the light of Calogero hypothesis. W
e also check that the hypothesis is compatible with the present bounds on t
he variations of fundamental constants and with the observed black body dis
tribution of the cosmic background radiation.