Holographic Bound in Quantum Field Energy Density and Cosmological Constant

Abstract

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.