A kinetic theory of diffusion in general relativity with cosmological scalar field

Abstract

A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It is shown that the energy-momentum tensor for this matter model is not divergence-free, which makes it inconsistent to couple the Fokker-Planck equation to the Einstein equations. This problem can be solved by postulating the existence of additional matter fields in spacetime or by modifying the Einstein equations. The case of a cosmological scalar field term added to the left hand side of the Einstein equations is studied in some details. For the simplest cosmological model, namely the flat Robertson-Walker spacetime, it is shown that, depending on the initial value of the cosmological scalar field, which can be identified with the present observed value of the cosmological constant, either unlimited expansion or the formation of a singularity in finite time will occur in the future. Future collapse into a singularity also takes place for a suitable small but positive present value of the cosmological constant, in contrast to the standard diffusion-free scenario.

17 pages, no figures. The present version corrects an erroneous statement on the physical interpretation of the results made in the original publication

References in corpus (6)

• Relativistic Brownian Motion
• The Einstein-Vlasov System/Kinetic Theory
• Relativistic diffusion processes and random walk models
• Relativistic diffusion
• Central Limit Theorem for a Class of Relativistic Diffusions
• Neutron Stars and the Cosmological Constant Problem

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• Cosmology with matter diffusion
• Cosmic evolution of dark energy in a generalized Rastall gravity
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• A thermodynamics revision of Rastall gravity
• Cosmological models with fluid matter undergoing velocity diffusion
• A transition between bouncing hyper-inflation to ΛCDM from diffusive scalar fields
• Does the diffusion DM-DE interaction model solve cosmological puzzles?
• Linear potentials in galaxy halos by Asymmetric Wormholes
• Realising Interactions Between Dark Matter and Dark Energy Using $k$-essence Cosmology
• Time-dependent diffusive interactions between dark matter and dark energy in the context of $k-$essence cosmology
• Evolution of a Simple Inhomogeneous Anisotropic Cosmological Model with Diffusion
• Analytical solutions of the geodesic equation in the space-time of a black hole surrounded by perfect fluid in Rastall theory
• Diffusive dark matter and dark energy scenario and $k-$essence in the context of Supernova Ia observations
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• Non-linear dark matter collapse under diffusion
• Dynamics of tilted Bianchi models of types III, IV, V in presence of diffusion
• A relation between diffusion,temperature and the cosmological constant
• Does diffusion mechanism favor the emergent scenario of the universe?
• Modified scaling in $k$-essence model in interacting dark energy - dark matter scenario
• Spacetime symmetries and geometric diffusion
• Matter Creation in Unimodular Gravity Cosmology