Exploring cosmic dynamics in Finsler–Randers model: Observational and dynamical system analysis

In this study, we consider the Finsler–Randers geometry model composed of standard matter, radiation and the cosmological constant-like dark energy. We explore the cosmic dynamics by using the dynamical system approach. This analysis reveals that the universe evolution composed of the decelerating and accelerating era will be explained in the model. In particular, the fixed points for the matter, radiation and the de Sitter era will exist in the model along with an additional fixed point for which the universe will evolve with [Formula: see text]. The observational estimation of model parameters involves the Bayesian analysis approach using the Markov Chain Monte Carlo method. The observational analysis highlight that the Finsler and [Formula: see text]CDM models may be indistinguishable from each other for [Formula: see text]. Although, for higher order values of [Formula: see text], the universe in the Finsler and [Formula: see text]CDM model may evolve differently.