Dynamical dark energy parametrizations in VCDM

In the context of a theory of minimally modified gravity, the $V(\ensuremath{\phi})$ cold dark matter (VCDM), one can realize any cosmological behavior at the level of the homogeneous and isotropic background without introducing fatal instabilities for perturbations. Therefore, VCDM provides a theoretically consistent and observationally testable framework of dynamical dark energy parametrizations with or without phantom behaviors. In this paper, we propose the VCDM realizations of various phenomenological parametrizations present in the literature: the Chevallier-Polarski-Linder, Barboza-Alcaniz, Jassal-Bagla-Padmanabhan, exponential, and logarithmic models. Using the VCDM equations for cosmological perturbations, we test them against the recent cosmological datasets, Planck 2018 and DESI baryon acoustic oscillation data release 2, and then discuss their implications.