Cosmological Landsberg Finsler spacetimes

TL;DR

This paper classifies all homogeneous and isotropic Landsberg-type Finsler spacetimes in four dimensions, identifying a unique non-Berwaldian Finsler generalization of the standard cosmological model with potential physical relevance.

Contribution

It provides the first classification of cosmological Landsberg Finsler structures and constructs a unique non-Berwaldian Finsler extension of FLRW geometry.

Findings

Identified viable non-stationary Landsberg Finsler spacetimes.

Proved that non-stationary Landsberg metrics are necessarily non-Berwaldian.

Constructed a unique Finsler generalization of FLRW geometry.

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.