Jeans analysis with κ-deformed Kaniadakis distribution in f (R) gravity

The influence of the κ-deformed Kaniadakis distribution on Jeans instability in the background of f(R) gravity is investigated, the dispersion relation considering the κ-deformed Kaniadakis distribution is derived by exploiting the kinetic theory. The cases of high and low frequency perturbations are analyzed, respectively, it is found that the range of the unstable modes and the growth rates decrease with the increased distribution index κ in both of high and low frequency regime. Finally, based on the derivation of effective temperature, the relation between Jeans mass and temperature is studied, it is found that lower Jeans mass means that the system is more likely to collapse due to gravitational instability, the system is unstable for lower distribution index κ.

The growth of structure

The growth of structure by gravitational collapse from initially small perturbations is described. The Jeans instability is calculated. The structure equations are obtained and solved in various cases (radiation-dominated, matter-dominated and others) via a linearized treatment. Hence the main features of the growth of density perturbations are obtained. The observed spectrum in the present is used to infer the primordial spectrum. The scale-invariant (Harrison-Zol’dovich) spectrum is described. The process of baryon acoustic oscillations is outlined and the sound horizon is defined. The chapter concludes with brief notes on galaxy formatiom.

Jeans Instability, Jeans Entropy and the Entropy Origin of Gravity

An entropic origin of gravity is re-visited. Isothermal self-gravitating cloud seen as an ideal gas is analyzed. Gravitational attraction within the isothermal cloud in equilibrium is balanced by the pressure, which is of a pure entropic nature. The notion of the Jeans entropy of the cloud corresponding to the entropy of the self-gravitating cloud in mechanical and thermal equilibrium is introduced. Balance of the gravitational compression and the entropic repulsion yields the scaling relation hinting to the entropic origin of the gravitational force. The analysis of the Jeans instability enables elimination of the “holographic screen” or “holographic principle” necessary for grounding of the entropic origin of gravity.

Higher-order generalized uncertainty principle corrections to the Jeans mass

The Jeans instability is regarded as an important tool for analyzing the dynamics of a self-gravitating system. However, this theory is challenging since astronomical observation data show some Bok globules, whose masses are less than the Jeans mass and still have stars or at least undergo the star formation process. To explain this problem, we investigate the effects of the higher-order generalized uncertainty principle on the Jeans mass of the collapsing molecular cloud. The results in this paper show that the higher order generalized uncertainty principle has a very significant effect on the canonical energy and gravitational potential of idea gas, and finally leads to a modified Jeans mass lower than the original case, which is conducive to the generation of stars in small mass Bok globules. Furthermore, we estimate the new generalized uncertainty principle parameter $$\gamma _0$$ γ 0 by applying various data of Bok globules, and find that the range of magnitude of $$\gamma _0$$ γ 0 is $${10^{11}} {-} {10^{12}}$$ 10 11 - 10 12 .