Cosmological Finsler Spacetimes

Abstract

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.

The kinetic gas universe

“…Finding solutions to the cosmological field equation sourced by the 1PDF of the matter content of the universe, and studying the resulting dynamics -in particular the possibility of modelling the accelerating expansion of the universe -is thus a primary goal. As a first step, one may search for solutions among the recently found class of cosmological Finsler Berwald spacetimes [11], for which the field equations simplify significantly [12].…”

Schwarzschild-like solutions in Finsler–Randers gravity

“…This is the GR limit for the energy-momentum tensor Y αβ . Finally, from (12) and (23) we conclude that in the GR limit the matter fields have no direct dependence on the nonlinear connection.…”

“…From the form of (1) it follows that √ |G| = √ −g √ −v, with g, v the determinants of the metrics g μν , v αβ respectively. This relation was used in (10)- (12). Equations (7)-(9) are derived from an extension of the Hilbert-Einstein action on the eight-dimensional Lorentz tangent bundle and constitute a generalization of the Einstein field equations of general relativity.…”

“…We will make some comments in order to give a physical interpretation in relation to the Eqs. (10)- (12). Lorentz violations produce anisotropies in the space and the matter sector.…”

“…Generalized Einstein field equations have been studied in the Finsler, Lagrange, generalized Finsler and Finsler-like spaces, for an osculating gravitational approach in which the second variable y(x) is a tangent/vector field [1][2][3] and in Finsler cosmology [4][5][6][7][8]. Different sets of generalized Einstein field equations were derived for the aforementioned spaces in the framework of a tangent bundle [9][10][11][12][13][14][15][16][17] and for the momentum space on the cotangent bundle [18][19][20][21][22][23]. Additionally, Lorentz invariance violation in Finsler/Finslerlike spacetime and in Finsler cosmology in very special relativity has also been studied in a large series of papers [5,[24][25][26][27].…”