$f$-mode oscillations of dark matter admixed quarkyonic neutron star

We systematically investigate $f-$mode oscillations ($\mathrm{\ell }$ = 2) in quarkyonic neutron stars with dark matter, employing the Cowling approximation within the framework of linearized general relativity. The relativistic mean-field approach is used to compute various macroscopic properties of neutron stars. The analysis focuses on three key free parameters in the model: transition density, QCD confinement scale, and dark matter (DM) Fermi momentum, all of which significantly affect the properties of $f-$mode oscillations. The inclusion of dark matter in quarkyonic equations of state leads to notable variations in $f-$mode frequencies. Despite these changes, several universal relations among the oscillation properties are found to hold, demonstrating their robustness in the presence of dark matter.