Rigorous proof of the slightly nonlinear Jeans instability in the expanding Newtonian universe
Abstract
Due to the nonlinearity of the EulerPoisson equations, it is possible that the nonlinear Jeans instability may lead to a faster density growing rate than the rate in the standard theory of linearized Jeans instability, which motivates us to study the nonlinear Jeans instability. The aim of this article is to develop a method proving the Jeans instability for slightly nonlinear EulerPoisson equations in the expanding Newtonian universe. The standard proofs of the Jeans instability rely on the Fourier analysis. However, it is difficult to generalize Fourier method to a nonlinear setting, and thus there is no result in the nonlinear analysis of Jeans instability. We firstly develop a nonFourierbased method to reprove the linearized Jeans instability in the expanding Newtonian universe. Secondly, we generalize this idea to a slightly nonlinear case. This method relies on the Cauchy problem of the Fuchsian system due to the recent developments of this system in mathematics. The fully nonlinear Jeans instability for the EulerPoisson and EinsteinEuler equations are in progress.
 Publication:

Physical Review D
 Pub Date:
 February 2022
 DOI:
 10.1103/PhysRevD.105.043519
 arXiv:
 arXiv:2201.01199
 Bibcode:
 2022PhRvD.105d3519L
 Keywords:

 Mathematics  Analysis of PDEs;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 21 pages