Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particular, we find the most general spatially homogeneous and isotropic Berwald spacetimes, which are Finsler spacetimes that can be regarded as closest to pseudo-Riemannian geometry. They are defined by a Finsler Lagrangian built from a zero-homogeneous function on the tangent bundle, which encodes the velocity dependence of the Finsler Lagrangian in a very specific way. The obtained cosmological Berwald geometries are candidates for the description of the geometry of the universe, when they are obtained as solutions from a Finsler gravity equation.

中文翻译：

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宇宙芬斯勒时空

将宇宙学原理应用于Finsler时空，我们确定了空间均匀且各向同性Finsler几何对称发生器的Lie代数，从而推广了Friedmann-Lemaître-Robertson-Walker几何。特别是，我们找到了最通用的空间均匀和各向同性的Berwald时空，它们是Finsler时空，可以被认为是最接近伪黎曼几何。它们是由Finsler Lagrangian定义的，该Finsler Lagrangian由切线束上的零均匀函数构建，该函数以非常特定的方式编码Finsler Lagrangian的速度相关性。当从芬斯勒引力方程中获得的宇宙学几何形式作为解时，所获得的宇宙学的伯瓦尔德几何形态可以作为描述宇宙几何形态的候选对象。