From quantum foam to graviton condensation: the Zel'dovich route

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtual particle-antiparticle pairs, supplemented with the Holographic Principle, we estimate the vacuum energy in a fairly reasonable agreement with the experimental values of the Cosmological Constant. We further highlight a connection between Wheeler's quantum foam and graviton condensation, as contemplated in the quantum $N$-portrait paradigm, and show that such connection also leads to a satisfactory prediction of the value of the cosmological constant. The above results suggest that the "unnaturally" small value of the cosmological constant may find a quite "natural" explanation once the nonlocal perspective of the large $N$-portrait gravitational condensation is endorsed.