Gibbons-Hawking Entropy and BMN Strings

TL;DR

The paper investigates whether quantum gravity imposes a universal finite bound on entropy accessible to an observer and how this may connect to the cosmological constant. It grounds the discussion in the Gibbons–Hawking entropy of de Sitter horizons and computes its magnitude for our universe, then contrasts it with other entropy sources, showing GH entropy as dominant. To test the bound, it formulates BMN strings in a pp-wave background and defines $S_m(g) = - \sum_n p_{n,m}(g)\log p_{n,m}(g)$ with $p_{m,n}(g) = |\langle m|\hat U(g)|n\rangle|^2$ and $g=\frac{J^2}{N}$, proving a lemma that uniform convergence of $p_n(g)$ to $\tilde p_n$ with $\sum_n \tilde p_n<1$ forces $S(g)$ to diverge under certain conditions, while arguing to exclude pathological measurement protocols. The work positions BMN strings as a concrete probe of the conjectured bound and highlights the potential to relate the bound to the observed value of $\Lambda$, offering a framework for future theoretical and (in principle) observational exploration of quantum-gravity entropy limits.

Abstract

We provide some up-to-date discussions related to cosmological event horizon and entropy of our universe, then introduce an intriguing idea that there may be a universal finite upper bound for entropy accessible to an observer in consistent theories of quantum gravity. We argue that the BMN (Berenstein-Maldacena-Nastase) strings provide a test of the idea and a possible estimate of the cosmological constant.