Cosmological Landsberg Finsler spacetimes

TL;DR

The paper tackles the problem of finding cosmological solutions within Finsler gravity by classifying all 4D, homogeneous and isotropic Landsberg spacetimes and isolating a unique non-Berwald unicorn that generalizes FLRW. It derives two Landsberg conditions for a cosmological ansatz $L(t,\,m{})=m{}^2 h(t,s)^2$, reveals six candidate branches, and shows that only one unicorn branch yields a viable spacetime, namely the L2-Lagrangian with a separated-variable, conformally separable form. This L2 generalization introduces a scale factor dynamics through a single time function $a(t)$ and a fixed parameter $f$, reducing the Finsler gravity equation to a cosmological system that recovers FLRW in the limit $f=-1$, while offering a distinct, time-asymmetric light-cone structure. The work provides a complete mathematical classification of 4D homogeneous and isotropic non-Berwald Landsberg geometries and sets the stage for future Finsler Friedmann equations and potential connections to dark matter and dark energy from a kinetic gas viewpoint.

Abstract

We locally classify all possible cosmological homogeneous and isotropic Landsberg-type Finsler structures, in 4-dimensions. Among them, we identify viable non-stationary Finsler spacetimes, i.e. those geometries leading to a physical causal structure and a dynamical universe. Noting that any non-stationary Landsberg metric must be actually non-Berwaldian (i.e., it should be a so-called 'unicorn'), we construct the unique Finsler, non-Berwaldian Landsberg generalization of Friedmann-Lemaitre-Robertson-Walker geometry.