Modified dynamics of dust Coulomb waves due to polarization force in gravitating viscoelastic fluid

We investigate the impact of the dust polarization force on linear dust Coulomb waves (DCWs) and gravitational (Jeans-type) instability in a dense, gravitating viscoelastic dusty plasma with high fugacity (𝑓 ≫ 1). In the low-fugacity limit (𝑓 ≪ 1), the system supports conventional dust acoustic waves (DAWs), while at high fugacity, DCWs emerge as the dominant mode due to strong inter-dust coupling and viscoelastic effects. The polarization force substantially modifies the DCW dispersion and amplifies the growth rate of gravitational instability. We derive modified instability criteria, highlighting that viscoelasticity tends to stabilize the system, whereas the polarization force has a destabilizing influence. These effects are particularly relevant to lunar dusty plasmas and diffuse astrophysical environments such as dust molecular clouds, where high dust fugacity and gravitational effects coexist. The analysis provides new insights into wave dynamics and structure formation in dense dusty plasmas.