May 12, 2025:
Dr. Christian Pfeifer
Affiliation: University of Bremen, Germany
Title: The gravitational field of kinetic gases and the accelerated expansion of the universe
Abstract: Kinetic gases provide a statistical description of large number multi-particle systems in terms of a 1-particle distribution function (1PDF) which encodes the dynamics of the system. Classically, the gravitational field of a kinetic gas is derived from the Einstein equations, with an energy momentum tensor that is derived from the 1PDF by averaging over all velocities. Hence, in the coupling between kinetic gases and spacetime geometry (gravity) only some specific aspects of the gas are taken into account, others are lost.
Pseudo-Finsler manifolds generalize pseudo-Riemannian manifolds in a straightforward manner. The geometry of a Finslerian manifold is derived from a general pseudo-norm, analogously to how the geometry of pseudo-Riemannian manifolds is derived from a metric.
In physics, pseudo-Finsler geometry is a viable and highly interesting candidate for an extended geometry of spacetime that can provide an improved description of gravitational interaction beyond general relativity, potentially offering a geometric understanding of dark matter and dark energy.
Finsler spacetime geometry offers a natural way to couple the kinetic gas without any averaging procedure to the geometry of spacetime, and thus, to determine the gravitational field of the kinetic gas taking all of its properties into account.
In this talk, I will discuss the Finsler gravity framework as extension of general relativity, and demonstrate that in homogeneous and isotropic symmetry, the Finsler gravity equation possesses solutions that describe an accelerated expanding universe, without the need of a cosmological constant or any other additional fields. I will introduce the concept of Finsler spacetimes and the Finsler gravity equation which couples Finsler geometry to kinetic gases. In homogeneous and isotropic symmetry, the Finsler gravity equation takes a Friedmann equation like form and allows for vacuum solutions that describe an exponentially expanding universe. This is a first direct indication that Finsler spacetimes are capable to address the nature of dark energy.