General parametrization for energy density of quintessence field

Abstract: We present a general parametrization for energy density of a quintessence field, a minimally coupled canonical scalar field which rolls down slowly during the late time. This parametrization can mimic all classes of quintessence dynamics, namely scaling-freezing, tracker and thawing dynamics for any redshift. For thawing dynamics the parametrization needs two free parameters while for scaling-freezing and tracker dynamics it needs at least four free parameters. More parameters make the model less interesting from the observational data analysis point of view but as we expect more precise data in future it may be possible to constrain the models with multiple free parameters which can tell about the dynamics more precisely. One of the main advantage of this parametrization is that it reduces the computational time to significant amount while mimicking the actual scalar field dynamics for all redshifts which may not be possible with other existing parametrizations. We compare the parametrization with two and four parameters with the standard $\Lambda$CDM model, $w$CDM and Chevallier-Polarski-Linder (CPL) parametrizations using cosmological observational data from Planck 2018 (distance priors), DESI $2024$ DR1, PantheonPlus, Hubble parameter measurements and the redshift space distortion. We find that the observational data prefers standard $\Lambda$CDM model over other models. If we allow phantom region then it is more preferred by the data compared to non-phantom thawing quintessence. Our analysis does not show any preference of the dynamical dark energy over a cosmological constant except for the CPL parametrization.