  We show that the use of suitable theorems for black hole formation in
Friedmann expanding universes leads to a modification of the Bekenstein-Hawking
entropy. By adopting an argument similar to the original Bekenstein one, we
write down the expression for the Bekenstein-Hawking entropy suitable for
non-static isotropic expanding universes together with the equation of state of
a black hole. This equation can be put in a form similar to the one of an ideal
gas but with a factor depending on the Hubble radius. Moreover, we give some
argument on a possible relation between our entropy expression and the
Cardy-Verlinde one. Finally, we explore the possibility that primordial
inflation is due to black hole evaporation in our context.
