Jeans analysis in fractional gravity

TL;DR

This paper explores the implications of fractional gravity on astrophysical phenomena, specifically Jeans instability, by extending classical and quantum models, and compares theoretical predictions with observations to constrain the theory.

Contribution

It introduces a generalized Lane-Emden equation in fractional gravity and assesses its validity through stability analysis and observational data comparison.

Findings

Constraints on fractional gravity parameters from Bok globule stability

Extension of Jeans instability analysis to fractional and quantum regimes

Derivation of a generalized Lane-Emden equation for fractional gravity

Abstract

It has recently been demonstrated [A. Giusti, Phys. Rev. D 101, 124029 (2020)] that characteristic traits of Milgrom's modified Newtonian dynamics (MOND) can be replicated from an entirely distinct framework: a fractional variant of Newtonian mechanics. To further assess its validity, this proposal needs to be tested in relevant astrophysical scenarios. Here, we investigate its implications on Jeans gravitational instability and related phenomena. We examine scenarios involving classical matter confined by gravity and extend our analysis to the quantum domain, through a Schr\"odinger-Newton approach. We also derive a generalized Lane-Emden equation associated with fractional gravity. Through comparisons between the derived stability criteria and the observed stability of Bok globules, we establish constraints on the theory's parameters to align with observational data.