  The Finsler-Randers space-time offers a novel perspective on cosmic dynamics,
departing from the constraints of General Relativity. This paper thoroughly
investigates two dark energy models resulting from the parametrization of $H$
within this geometric framework. We have conducted some geometrical and
physical analysis of the dark energy models in Finslerian geometry. First, We
have derived the field equations governing the universe's evolution within the
Finsler-Randers formalism, incorporating the presence of dark energy. Through
this, we explore its implications on cosmological phenomena, including cosmic
expansion, late-time behavior of the universe, cosmological phase transition,
and a few more. Also, we employ observational data such as Cosmic Chronometer,
Supernovae, Gamma-Ray Bursts, Quasar, and baryon acoustic oscillations to
constrain the parameters associated with dark energy in the Finsler-Randers
universe. Comparing theoretical predictions with empirical observations, we
assess the model viability and discern any deviations from the standard
$\Lambda$CDM cosmology. Our findings offer intriguing insights into the nature
of dark energy within this alternative gravitational framework, providing a
deeper understanding of its role in shaping cosmic evolution. The implications
of our results extend to fundamental cosmology, hinting at new avenues for
research to unravel the mysteries surrounding dark energy and the geometric
structure of the universe within non-standard gravitational theories.
