https://doi.org/10.1140/epjc/s10052-022-10318-9
Regular Article - Theoretical Physics
Dark energy and accelerating cosmological evolution from osculating Barthel–Kropina geometry
1
Faculty of Science and Industrial Technology, Prince of Songkla University, Surat Thani Campus, 84000, Surat Thani, Thailand
2
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN-HH), 077125, Bucharest, Romania
3
Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084, Cluj-Napoca, Romania
4
Astronomical Observatory, 19 Ciresilor Street, 400487, Cluj-Napoca, Romania
5
Department of Biology, School of Biological Sciences, Tokai University, 005-8600, Sapporo, Japan
6
Graduate School of Science and Technology, Physical and Mathematical Sciences, Tokai University, 005-8600, Sapporo, Japan
Received:
9
February
2022
Accepted:
9
April
2022
Published online:
29
April
2022
Finsler geometry is an important extension of Riemann geometry, in which each point of the spacetime manifold is associated with an arbitrary internal variable. Two interesting Finsler geometries with many physical applications are the Randers and Kropina type geometries. A subclass of Finsler geometries is represented by the osculating Finsler spaces, in which the internal variable is a function of the base manifold coordinates only. In an osculating Finsler geometry, we introduce the Barthel connection, with the remarkable property that it is the Levi–Civita connection of a Riemannian metric. In the present work we consider the gravitational and cosmological implications of a Barthel–Kropina type geometry. We assume that in this geometry the Ricci type curvatures are related to the matter energy–momentum tensor by the standard Einstein equations. The generalized Friedmann equations in the Barthel–Kropina geometry are obtained by considering that the background Riemannian metric is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equation is also derived. The cosmological properties of the model are investigated in detail, and it is shown that the model admits a de Sitter type solution and that an effective dark energy component can also be generated. Several cosmological solutions are also obtained by numerically integrating the generalized Friedmann equations. A comparison of two specific classes of models with the observational data and with the standard 
CDM model is also performed, and it is found that the Barthel–Kropina type models give a satisfactory description of the observations.
© The Author(s) 2022
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