Kinetic Jeans instability in FOG framework

The key mechanism triggering the complex dynamics of astrophysical structure formation in extensive evolutionary clouds is indeed sourced in the non-local gravitational (Jeans) instability. Motivated by recent astrophysical observations, establishing the growth of large-scale structures in the Universe, we herein propose a kinetic theory-based Jeans instability formalism in the fourth order gravity (FOG) framework. The analysis is modelled with the help of the canonical Boltzmann transport equation coupled with the FOG-modified Poisson equation. Our main goal lies in the inclusion of a scale-dependent free length parameter [Formula: see text] sourced in the FOG theory and its effects on the instability. The L-parameter governs the extent of the higher-order gravitational corrections over the classical Newtonian picture. Applying a standard local normal mode analysis, we derive the FOG-modified generalized linear dispersion relation. The dispersion analysis enables us to derive the critical Jeans mass for various structure-forming complex astroclouds, including Bok globules, diffuse molecular clouds, and giant molecular clouds. Interestingly, the resulting FOG-modified Jeans mass displays a non-monotonic density-dependency at larger [Formula: see text]-values. This new gravitational behaviour restricts small-scale collapse, while promoting massive fragmentation, thereby leading to a preferentially smoother formation of large-scale structures without the inclusion of dark energy and dark matter. Our analysis has potential implications for the emergence of stellar mass distributions through the Jeans instability mechanism, with applicability in diverse astrophysical environments, fairly supported with real astronomical observations.