A spherical hydrodynamical model of cosmic voids in {\Lambda}CDM and beyond

Cosmic voids have emerged as powerful probes for cosmology, providing complementary information on the large-scale structure of the universe. We present the first application of a hydrodynamical framework to model the evolution of cosmic voids. This approach offers a physically intuitive characterization of void dynamics and can naturally be applied to non-standard cosmologies. We derive the cosmology-dependent mapping that relates the linear (Lagrangian) and fully non-linear (Eulerian) evolution of the matter density contrast, a central component for accurate theoretical modeling of void statistics. Furthermore, we present a new method for determining the shell-crossing epoch across arbitrary cosmological backgrounds, thereby extending previous treatments restricted to the Einstein-de Sitter universe. Motivated by recent DESI results hinting at dynamical dark energy, we investigate void evolution in $w_0w_a$CDM cosmologies by varying $w_0$ and $w_a$. We also consider the impact of varying the matter density parameter, $\Omega_{\mathrm{m},0}$. We find that the evolution of isolated, spherically symmetric cosmic voids is most sensitive to $\Omega_{\mathrm{m},0}$ and $w_0$, which can alter the non-linear density contrast by up to 20-30%. Variations in $w_a$ have a smaller impact, but may still lead to measurable effects. We also show that the cosmology-dependent mapping between linear and non-linear density contrasts may provide a sensitive probe of dynamical dark energy in precision void analyses.