Relativistic Diffusing Particles, Entropy and Varying Cosmological Constants

We discuss Einstein equations with a non-conserved energy-momentum Tμν. The energy-momentum tensor T˜μν on the right hand side of Einstein equations is expressed in the form 8πGTμν−gμνΛ+Σμν where G is the Newton constant, Λ is the cosmological term and Tμν is the energy-momentum of an ideal fluid. The remaining part Σμν describes the viscosity and a heat flow. We discuss space-time-dependent Newton “constant” G and the cosmological term Λ. The covariant conservation law for T˜μν imposes a relation between the energy-momentum (non)conservation and the variation of G and Λ. The covariant derivative ∇μTμν can be related to the first law of thermodynamics and expressed by the temperature T and the entropy S. The energy-momentum non-conservation in our models is a consequence of a diffusion of its constituting particles. We describe a gas of diffusing massive particles in a homogeneous isotropic space-time as a system with a time-dependent linear barotropic equation of state Pt=wtρt with 0<wt≤13. The gas of massive diffusing particles in an expanding universe tends in a limit of infinite time to the gas of diffusing massless particles. We obtain results on the energy density, entropy and phase space dstribution in a soluble model of massless relativistic particles in a spatially flat expanding universe.