Confirmation of accelerated expansion of the Universe probed the concept of dark energy theory, and since then, numerous models have been introduced to explain its origin and nature. The present work is based on reconstructing dark energy by parametrization of the deceleration parameter in the FLRW universe filled with radiation, dark matter and dark energy. We have chosen some well-motivated parametrized models 1-3 in an attempt to investigate the energy density in terms of deceleration parameters by estimating the cosmological parameters with the help of different observational datasets. Also, we have introduced a new model 4 for the parametrization of the deceleration parameter. Then we analyzed the cosmography parameters using the best-fit values of the parameters. Using the information criteria, we have examined the viability of the models.

In this study, the non-metricity scalar Q, which characterizes the gravitational interaction, is used to analyze the Universe’s rapid expansion within the context of the f(Q) gravity theory. We suggest an emergent scale factor, which produces the deceleration parameter in redshift form which determines the solution of the field equations in the FLRW Universe. We evaluate the appropriate values of the model parameters by considering SNIa from Pantheon, CMB from Planck 2018, BAO, and 36 data points from Hubble datasets using Markov Chain Monte Carlo approach. The deceleration parameter’s development suggests that the Universe is moving from its deceleration phase into its acceleration phase. Furthermore, we analyze the statefinder (r, s) diagnostic parameter. We also use some different forms of f(Q) gravity models to study some other cosmological parameters, i.e. f ( Q ) = α 1 Q , f ( Q ) = α 2 Q m and f ( Q ) = α 3 Q m + Q , where α ₁, α ₂, α ₃ and m all are free model parameters. Finally, we concluded that all f(Q) models predict that at z = 0, Universe is in the phase of accelerating and behaves like the quintessence models and at z = − 1 , approaches to ΛCDM models.

We further investigate the dark energy model based on the Finsler geometry inspired osculating Barthel–Kropina cosmology. The Barthel–Kropina cosmological approach is based on the introduction of a Barthel connection in an osculating Finsler geometry, with the connection having the property that it is the Levi-Civita connection of a Riemannian metric. From the generalized Friedmann equations of the Barthel–Kropina model, obtained by assuming that the background Riemannian metric is of the Friedmann–Lemaitre–Robertson–Walker type, an effective geometric dark energy component can be generated, with the effective, geometric type pressure, satisfying a linear barotropic type equation of state. The cosmological tests, and comparisons with observational data of this dark energy model are considered in detail. To constrain the Barthel–Kropina model parameters, and the parameter of the equation of state, we use 57 Hubble data points, and the Pantheon Supernovae Type Ia data sample. The st statistical analysis is performed by using Markov Chain Monte Carlo (MCMC) simulations. A detailed comparison with the standard $$\Lambda $$Λ CDM model is also performed, with the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) used as the two model selection tools. The statefinder diagnostics consisting of jerk and snap parameters, and theOm(z) diagnostics are also considered for the comparative study of the Barthel–Kropina and $$\Lambda $$Λ CDM cosmologies. Our results indicate that the Barthel–Kropina dark energy model gives a good description of the observational data, and thus it can be considered a viable alternative of the $$\Lambda $$Λ CDM model.