Thermodynamic properties of γ fluids and the quantum vacuum

Abstract

The thermodynamic behavior of a relativistic perfect simple fluid obeying the equation of state p=(\ensuremath{\gamma}-1)\ensuremath{\rho}, where 0\ensuremath{\le}\ensuremath{\gamma}\ensuremath{\le}2 is a constant, is investigated. Particular cases include a vacuum (p=-\ensuremath{\rho},\ensuremath{\gamma}=0), random cosmic strings (p=-1/3\ensuremath{\rho},\ensuremath{\gamma}=2/3), black-body radiation (p=1/3\ensuremath{\rho},\ensuremath{\gamma}=4/3), and stiff matter (p=\ensuremath{\rho},\ensuremath{\gamma}=2). Fluids with \ensuremath{\gamma}1 become hotter when they expand adiabatically (T\ensuremath{\propto}${\mathit{V}}^{1\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$). By assuming that such fluids may be regarded as a kind of generalized radiation, the general Planck-type form of the spectrum is deduced. As a limiting case, a new Lorentz-invariant spectrum of the vacuum which is compatible with the equation of state and other thermodynamic constraints is proposed. Some possible consequences to early universe physics are also discussed.