Based on the framework of Kaniadakis’ statistics and its related kinetic theory, the Jeans instability for self-gravitational systems in the background of Eddington-inspired Born–Infield (EiBI) gravity is revisited. A dispersion relation generalizing the Jeans modes is derived by modifying the Maxwellian distribution to a family of power law distributions parameterized by the κ parameter. It is established that the κ-deformed Kaniadakis distribution has significant effects on the Jeans modes of the collisionless EiBI-gravitational systems. And as expected, in the limitation κ → 0, the corresponding results for Maxwellian case are recovered. The related result in the present work is valuable for the investigations involving the fields of astrophysics such as neutron stars, accretion disks, and relevant plasma physics, etc.

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In the present paper, the dispersions and Landau damping of the ion acoustic waves in the dark plasma system with non-extensive distributed millicharged dark matter particles are investigated under the kinetic theory regimes. The result shows that the peculiarities of the Landau damping of the waves depend on the parameter q of the distribution function. However, the growth rate due to the streaming dark matter is acutely tiny compared to the damping rates arising from the electrons and ions. As a result, both Maxwellian and non-extensive distributions are strongly damped by the dark matter. Hence, the waves cannot be stimulated yet.

The possibility of baryons cooled by a millicharged dark matter (mDM) via mDM-baryons scattering has recently been proposed to explain the observation discrepancy from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES). In this sense, we analyze the Jeans instability of self-gravitational systems in the background of mDM under kinetic regime that the collisionless Boltzmann equation and Poisson equation have been combined to obtain the modified dispersion relation. It is shown that the effect of mDM is significant on the dynamics of gravitational collapse, i.e., the presence of mDM makes the self-gravitational systems more difficult to collapse relatively.