A statistical representation of the cosmological constant from finite size effects at the apparent horizon

In this paper we present a statistical description of the cosmological constant in terms of massless bosons (gravitons). To this purpose, we use our recent results implying a non vanishing temperature T-Lambda for the cosmological constant. In particular, we found that a non vanishing T-Lambda allows us to depict the cosmological constant Lambda as composed of elementary oscillations of massless bosons of energy h omega by means of the Bose-Einstein distribution. In this context, as happens for photons in a medium, the effective phase velocity v(g) of these massless excitations is not given by the speed of light c but it is suppressed by a factor depending on the number of quanta present in the universe at the apparent horizon. We found interesting formulas relating the cosmological constant, the number of quanta N and themean value (lambda) over bar of the wavelength of the gravitons. In this context, we study the possibility to look to the gravitons system so obtained as being very near to be a Bose-Einstein condensate. Finally, an attempt is done to write down the Friedmann flat equations in terms of N and (lambda) over bar.