A Cosmological Unicorn Solution to Finsler Gravity

Abstract

We present a new family of exact vacuum solutions to Pfeifer and Wohlfarth's field equation in Finsler gravity, consisting of Finsler metrics that are Landsbergian but not Berwaldian, also known as unicorns due to their rarity. Interestingly we find that these solutions have a physically viable light cone structure, even though in some cases the signature is not Lorentzian but positive definite. We furthermore find a promising analogy between our solutions and classical FLRW cosmology. One of our solutions in particular has cosmological symmetry, i.e. it is spatially homogeneous and isotropic, and it is additionally conformally flat, with the conformal factor depending only on the timelike coordinate. We show that this conformal factor can be interpreted as the scale factor, we compute it as a function of cosmological time, and we show that it corresponds to a linearly expanding (or contracting) Finsler universe.

References in corpus (10)

• Planck-scale modified dispersion relations and Finsler geometry
• The General Very Special Relativity in Finsler Cosmology
• Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis
• Relativistic kinetic gases as direct sources of gravity
• Foundations of Finsler spacetimes from the Observers' Viewpoint
• The connections of pseudo-Finsler spaces
• The kinetic gas universe
• On the analyticity of static solutions of a field equation in Finsler gravity
• Radar orthogonality and radar length in Finsler and metric spacetime geometry
• Canonical variational completion of differential equations

Cited by in corpus (3)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Cosmological Landsberg Finsler spacetimes
• Finslerian geometrodynamics