Background gravitational waves as signature of the adiabatic expansion of a black body that represents the dark universe

Abstract

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature $T$ in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy represented by the vacuum energy, being quantized into virtual particles with extremely small masses that form such gas representng the own tissue of the expanding space-time governed by a negative pressure whose origin is the equation of state (EOS) of vacuum, i.e., $p=-\rho$, where $\rho$ is the vacuum energy density. So, each vacuum particle occupies a tiny area of space so-called Planck area $L_p^{2}$, which represents the minimum area of the whole space-time given by the spherical surface with area $4\pi R_H^2$, where $R_H$ is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the very small order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of $10^{-17}$Hz due to the slight stretching of the fabric of space-time.