Statistical description of massless excitations within a sphere with a linear equation of state and the dark energy case

Abstract: In this paper we continue the investigations present in \cite{1}-\cite{3}. In particular, we extend the theorem proved in \cite{3} to any massless excitation in a given spherical box. As a first interesting result, we show that it is possible, contrary to the black hole case studied in detail in \cite{1,2,3}, to build macroscopic configurations with a dark energy equation of state. To this purpose, by requiring a stable configuration, a macroscopic dark fluid is obtained with an internal energy $U$ scaling as the volume $V$, but with a fundamental correction looking like $\sim 1/R$ motivated by quantum fluctuations. Thanks to the proposition in section 3 (and in \cite{3} for gravitons), one can depict the dark energy in terms of massless excitations with a discrete spectrum. This fact open the possibility to test a possible physical mechanism converting usual radiation into dark energy in a macroscopic configuration, also in a cosmological context. In fact, for example, in a Friedmann flat universe with a cosmological constant particles are marginally trapped at the Hubble horizon for any given comoving observer.