From kinetic gases to an exponentially expanding universe — the Finsler-Friedmann equation

Abstract

We investigate the gravitational field of a kinetic gas beyond its standard derivation from the second moment of the one-particle distribution function (1PDF), which typically serves as the energy-momentum tensor in the Einstein equations. This standard procedure raises an important question: why do the other moments of the 1PDF (which are needed to fully characterize the kinematical properties of the gas) not contribute to the gravitational field? Moreover, could these moments be relevant in addressing the dark energy problem? Using the canonical coupling of the full 1PDF to Finsler spacetime geometry via the Finsler gravity equation, we show that in general all moments contribute non-trivially. We derive the Finsler gravity equation in homogeneous and isotropic symmetry in conformal time — dubbed the Finsler-Friedmann equation — which determines both the scale factor and the causal structure dynamically. Remarkably, this equation naturally admits a vacuum solution describing an exponentially expanding spacetime, without requiring a cosmological constant or any additional quantities. The resulting causal structure is a mild deformation of the one of Friedmann-Lemaître-Robertson-Walker (FLRW) geometry; close to the rest frame defined by cosmological time (i.e. for slowly moving objects), the causal structures of the two geometries are nearly indistinguishable.