Gravitons in a Box

TL;DR

This paper establishes a universal bound on the number of gravitons in a given region, linking it to matter mass and gravitational entropy, and shows it saturates the Bekenstein bound, with implications for the observable universe.

Contribution

It introduces a universal bound on graviton number based on matter properties and demonstrates its relation to gravitational entropy and the Bekenstein bound.

Findings

The number of gravitons is bounded by (m/Mp)^2.

Graviton number saturates the Bekenstein entropy bound.

The bound is robust against initial matter states.

Abstract

Gravity and matter are universally coupled, and this unique universality provides us with an intriguing way to quantifying quantum aspects of space-time in terms of the number of gravitons within a given box. In particular, we will provide a limit on the number of gravitons if we trace out the matter degrees of freedom. We will 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 signify the number of bosonic states they occupy, the number of gravitons will place an indirect constraint on the gravitational entropy of the system. We will show that it saturates Bekenstein bound on the gravitational Area-law of entropy. We will also find that our conclusion is quite robust against the initial state of the matter degrees of freedom. Based on these observations, we will ascertain that the gravitons permeating in the observable Universe always $N_g\gg 1$.