Anisotropic universe with anisotropic dark energy

We investigate the anisotropic parametrization of the dark energy equation of state within the framework of an axisymmetric (planar) Bianchi-I universe. Using the latest $\mathrm{Pantheon}+$ Type Ia Supernova dataset, augmented by SH0ES Cepheid distance calibrators, we constrain both the equation of state for anisotropic dark energy and other standard cosmological parameters. Additionally, we examine the presence of an underlying anisotropic axis. Our analysis yields a mean anisotropic dark energy equation of state as $\overline{w}=\ensuremath{-}0.8{6}_{\ensuremath{-}0.11}^{+0.15}$ and a difference in the equation of states in and perpendicular to the plane of the axisymmetric Bianchi-I space-time as ${\ensuremath{\delta}}_{w}=\ensuremath{-}0.12{9}_{\ensuremath{-}0.064}^{+0.090}$. We also identify an axis of anisotropy at approximately $(272\ifmmode^\circ\else\textdegree\fi{},21\ifmmode^\circ\else\textdegree\fi{})$ in galactic coordinates. Through a comparative study of different cosmological models, we find that the data favor a Bianchi-I universe with anisotropic dark energy, where the equation of state deviates from ``$\ensuremath{-}1$'' along the axis of anisotropy (the ${w}_{b}\mathrm{CDM}$ model), over other anisotropic models considered and the standard flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ or $w\mathrm{CDM}$ models.