  The cosmological constant problem is reanalyzed by imposing the limitation of
the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the
calculation of the energy density of a field theory. It is shown that if a
quantum field theory has to be consistent with gravity and holography, i.e.
with an upper limit of storing information in a given area, the ultraviolet
momentum cut-off is not the Planck mass, M_p, as naively expected, but
M_p/N_U^(1/4) where N_U is the number of d.o.f. of the universe. The energy
density evaluation turns out completely consistent with Bousso's bound on the
cosmological constant value. The scale M_p/N_U^(1/4), that in the "fat
graviton" theory corresponds to the graviton size, originates by a selfsimilar
rearrangement of the elementary d.o.f. at different scales that can be seen as
an infrared-ultraviolet connection.
