A statistical representation of the cosmological constant from finite size effects at the apparent horizon

TL;DR

This paper models the cosmological constant as a statistical system of massless bosons (gravitons) with a non-zero temperature, exploring their collective behavior and potential Bose-Einstein condensation near the apparent horizon.

Contribution

It introduces a novel statistical framework for the cosmological constant using massless bosons and relates it to quantum properties like wavelength and quanta number, including a reformulation of Friedmann equations.

Findings

Cosmological constant can be described by a Bose-Einstein distribution of gravitons.

Effective phase velocity of gravitons is reduced depending on quanta number.

Formulas relate the cosmological constant, quanta number, and graviton wavelength.

Abstract

In this paper we present a statistical description of the cosmological constant in terms of massless bosons (gravitons). To this purpose, we use our recent results implying a non vanishing temperature ${T_{\Lambda}}$ for the cosmological constant. In particular, we found that a non vanishing $T_{\Lambda}$ allows us to depict the cosmological constant $\Lambda$ as composed of elementary oscillations of massless bosons of energy $\hbar\omega$ by means of the Bose-Einstein distribution. In this context, as happens for photons in a medium, the effective phase velocity $v_g$ of these massless excitations is not given by the speed of light $c$ but it is suppressed by a factor depending on the number of quanta present in the universe at the apparent horizon. We found interesting formulas relating the cosmological constant, the number of quanta $N$ and the mean value $\overline{\lambda}$ of the wavelength of the gravitons. In this context, we study the possibility to look to the gravitons system so obtained as being very near to be a Bose-Einstein condensate. Finally, an attempt is done to write down the Friedmann flat equations in terms of $N$ and $\overline{\lambda}$.