The kinetic gas universe

Abstract

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However, when the gravitational field of a kinetic gas is derived via the Einstein-Vlasov equations, the information about the velocity distribution of the gas particles is averaged out and therefore lost. We propose to derive the gravitational field of a kinetic gas directly from its 1PDF, taking the velocity distribution fully into account. We conjecture that this refined approach could possibly account for the observed dark energy phenomenology.

Cosmological evolution and dark energy in osculating Barthel–Randers geometry

“…In order to investigate the cosmological implications of the Barthel-Randers geometry, given by the Barthel-Randers model, we assume that the Riemannian metric g i j (x) is given by the Friedmann-Lemaitre-Robertson-Walker metric (75).…”

“…This fact follows naturally from the construction of the Randers metric. In this way we conserve in the Finslerian extension of general relativity one of the essential features of the cosmological Friedmann-Lemaitre-Robertson-Walker metric (75).…”

“…(75), we need to calculate the Ricci tensor and the Ricci scalar, respectively. In Riemannian geometry the Christoffel symbols are defined as On the other hand, by writing in components formula (B1) for the metric g I J in (75), it is elementary to see that the non-vanishing components are…”

“…These field equations can be obtained by varying with respect to L the action S[L] = ⊂T M vol( )R | , where = {(x,ẋ) ∈ T M|F(x,ẋ) = 1} denotes the unit tangent bundle, while vol( ) is the volume form on , obtained by using the Finsler metric. An approach to investigating general relativistic kinetic gas theory by using methods from Finsler geometry was introduced in [75].…”

Randerspp-waves

“…Hence, although the velocity distribution of the gas is taken into account for its dynamics, it is averaged away when determining the gas gravitational field. A direct coupling of the gas 1PDF to Finsler geometry circumvents this loss of information and gives rise to a gas gravitational field distribution described by Finsler geometry [11,12].…”