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The presence of heavy baryons, such as $\Delta$-baryons and hyperons cansignificantly impact various properties of Neutron Stars (NSs), likeoscillation frequencies, dimensionless tidal deformability, mass, and radii. Weexplored these effects within the Density-Dependent Relativistic Mean Fieldformalism. Our analysis considered $\Delta$-admixed NS matter in bothhypernuclear and hyperon-free scenarios, providing insights into particlecompositions and their effects on NS properties. Our study of non-radial$f$-mode oscillations revealed a distinct increase in frequency due to theadditional baryons. The degree of increase was significantly influenced by themeson-baryon coupling strengths. Notably, the coupling between$\Delta$-resonances and $\sigma$-mesons played a highly influential role. Insome cases, it led to an approximately 20\% increase in the $f$-modeoscillation frequency of canonical NSs. These couplings also affect other bulkproperties of NSs, including mass, radii, and dimensionless tidal deformability($\Lambda$). Comparing our results with available observational data frompulsars (NICER) and gravitational waves (LIGO-VIRGO collaboration), we foundstrong agreement, particularly concerning $\Lambda$.

Probing the impact of Delta-Baryons on Nuclear Matter and Non-Radial Oscillations in Neutron Stars