  The pulsational mode of gravitational collapse (PMGC) originating from the
combined gravito-electrostatic interaction in complex dust molecular clouds
(DMCs) is a canonical mechanism leading to the onset of astronomical structure
formation dynamics. A generalized semi-analytic model is formulated to explore
the effects of the Eddington-inspired Born-Infeld (EiBI) gravity, non-thermal
(r, q)-distributed electrons, and dust-polarization force on the PMGC stability
concurrently. The thermal ions are treated thermo-statistically with the
Maxwellian distribution law and the non-thermal electrons with the (r,
q)-distribution law. The constitutive partially ionized dust grains are modeled
in the fluid fabric. A spherical normal mode analysis yields a generalized
linear PMGC dispersion relation. Its oscillatory and propagation
characteristics are investigated in a reasonable numerical platform. It is
found that an increase in the polarization force and positive EiBI parameter
significantly enhances the instability, causing the DMC collapse and vice
versa. The electron non-thermality spectral parameters play as vital
stabilizing factors, and so on. Its reliability and applicability are finally
outlined in light of astronomical predictions previously reported in the
literature.
