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 Refs. 1–3. In particular, we extend the theorem proved in Ref. 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 Refs. 1–3, 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 [Formula: see text] scaling as the volume [Formula: see text], but with a fundamental correction looking like [Formula: see text] motivated by quantum fluctuations. Thanks to the proposition in Sec. 3 (and in Ref. 3 for gravitons), one can depict the dark energy in terms of massless excitations with a discrete spectrum. This fact opens 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.