The kinetic gas universe
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Letter
The kinetic gas universe Manuel Hohmann1,a , Christian Pfeifer1,b , Nicoleta Voicu2,c 1 2
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Str. 50, 500091 Brasov, Romania
Received: 13 June 2020 / Accepted: 23 August 2020 © The Author(s) 2020
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.
1 Kinetic gases instead of perfect fluids Numerous gravitating physical systems are described by a perfect fluid, for instance: neutron and ordinary stars, accretion discs, gas planets and last, but not least, the universe as a whole - which is our main subject of interest. Their properties are encoded in a (perfect) fluid energy momentum tensor T ab = ( p + ρ)U a U b + g ab p,
(1)
composed of the density ρ, the pressure p, the average propagation direction of the fluid U and the spacetime metric g, supplemented by an equation of state relating energy density and pressure. The dynamics of the system are derived from the Euler equations ∇a T ab = 0; the gravitational field is determined by the Einstein equations: G ab =
8π G ab T . c4
a e-mail:
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(2)
b e-mail:
[email protected] (corresponding author)
c e-mail:
[email protected]
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Solving the Einstein equations in homogeneous and isotropic symmetry, and interpreting the perfect fluid energymomentum tensor as the one describing the matter content of the whole universe, yields the standard model of cosmology and predicts the existence of ∼ 72% dark energy, ∼ 23% dark matter and only ∼ 5% visible matter as constituents of the universe. A more fundamental way to describe the dynamics of a fluid, is to understand the multiple particle system which constitutes the fluid as a kinetic gas [1]. In this approach, all the information about the system is stored in a 1-particle distribution function (1PDF), φ(x, x). ˙ It encodes how many gas particles at a given spacetime point x propagate on worldlines with normalized 4-velocity x˙ = ddτx . The dynamics of the kinetic gas are derived from a time evolution equation along all possible particle trajectories, ∂φ ∂φ dφ = a x˙ a + a x¨ a = C, dτ ∂x ∂ x˙
(3)
where C is called the collision curr
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