Gravitons in a box

Gravity and matter are universally coupled, and this unique universality provides us with an intriguing way to quantify quantum aspects of space-time in terms of the number of gravitons within a given box. In particular, we provide a limit on the number of gravitons if we trace out the matter degrees of freedom. We obtain the universal bound on the number of gravitons, which would be given by $N_g\approx (m/M_p{)}^2$. Since the number of gravitons also signifies the number of bosonic states they occupy, the number of gravitons indirectly constrain the system’s gravitational entropy. We show that it saturates the Bekenstein bound on the gravitational area law of entropy. Based on these observations, we ascertain that the gravitons permeating in the observable Universe are always $N_g\gg 1$.