Imprints of an extended Chevallier-Polarski-Linder parametrization on the large scale of our universe

In the present work we perform a systematic analysis of a new dark energy parametrization and its various corrections at first and higher orders around the presence epoch $z=0$, where the first order correction of this dark energy parametrization recovers the known Chevallier-Polarski-Linder model. We have considered up to the third order corrections of this parametrization and investigate the models at the level of background and perturbations. The models have been constrained using the latest astronomical datasets from a series of potential astronomical data, such as the cosmic microwave background observations, baryon acoustic oscillations measurements, recent Pantheon sample of the supernova type Ia and the Hubble parameter measurements. From the analyses we found that all parametrization favor the quintessential character of the dark energy equation of state where the phantom crossing is marginally allowed (within 68\% CL). Finally, we perform the Bayesian analysis using \texttt{MCEvidence} to quantify the statistical deviations of the parametrizations compared to the standard $\Lambda$CDM cosmology. The Bayesian analysis reports that $\Lambda $CDM is favored over all the DE parametrizations.