Some properties and implications of the creation pressure and the generalized equilibrium: modification of the adiabatic index, cosmological perturbations

Abstract

The creation pressure, due to constant specific entropy particle production, vanishes for a fluid where the sum of the energy density and the isotropic pressure is zero; for example in an empty space–time with the cosmological constant interpreted as vacuum energy density. Within the framework of relativistic thermodynamics theories, the energy–momentum tensor of a linear barotropic fluid with constant specific entropy particle production and in generalized equilibrium can be written as the effective energy–momentum tensor of a perfect linear barotropic fluid where the adiabatic index is a homographic function of the initial adiabatic index. This function shows that by adding constant specific entropy particle production to a phantom fluid, the effective perfect fluid will be without phantom property, whereas there are some fluids that with specific entropy particle production have phantom property. This transformation is useful for obtaining the behaviour of the scale factor of cosmological models. By solving the equation that comes from the entropy production equation, then the transport equation in the framework of the Muller-Israel-Stewart second-order causal relativistic thermodynamics, assuming constant specific entropy particle production and the generalized equilibrium, we obtain the bulk viscosity coefficient ζ and the relaxation time τ. The relation ζ ∝ $$ \rho^{{\frac{1}{2}}} $$ between ζ and the energy density ρ is predicted in spatially flat homogeneous and isotropic (FLRW) cosmological model for any value of the constant state parameter. The gauge–invariant energy density contrast and velocity perturbations of the previous cosmological model in the matter-dominated era with isentropic particle production are studied. The modes of these perturbations are decaying faster than the corresponding modes for the perfect fluid perturbations in the particle number conservation case. Then the isentropic, usually called adiabatic, gauge–invariant energy density contrast and velocity perturbations in case of a perfect linear barotropic fluid with particle number conservation are studied, in particular for negative values of the constant state parameter.