https://doi.org/10.1140/epjc/s10052-024-12924-1
Regular Article - Theoretical Physics
Finsler–Randers–Sasaki gravity and cosmology
1
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784, Athens, Greece
2
National Observatory of Athens, Lofos Nymfon, 11852, Athens, Greece
3
CAS Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China, 230026, Hefei, Anhui, China
4
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
5
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 15784, Athens, Greece
Received:
12
January
2024
Accepted:
15
May
2024
Published online:
28
May
2024
We present for the first time a Friedmann-like construction in the framework of an osculating Finsler–Randers–Sasaki (F–R–S) geometry. In particular, we consider a vector field in the metric on a Lorentz tangent bundle, and thus the curvatures of horizontal and vertical spaces, as well as the extra contributions of torsion and non-linear connection, provide an intrinsic richer geometrical structure, with additional degrees of freedom, that lead to extra terms in the field equations. Applying these modified field equations at a cosmological setup we extract the generalized Friedmann equations for the horizontal and vertical space, showing that we obtain an effective dark energy sector arising from the richer underlying structure of the tangent bundle. Additionally, as it is common in Finsler-like constructions, we obtain an effective interaction between matter and geometry. Finally, we consider a specific model and we show that it can describe the sequence of matter and dark-energy epochs, and that the dark-energy equation of state can lie in the quintessence or phantom regimes, or cross the phantom divide.
© The Author(s) 2024
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