Jeans instability in an expanding universe with dissipation

TL;DR

This paper investigates Jeans instability in an expanding universe using the BGK model, revealing how dissipation affects the growth and oscillation of density perturbations.

Contribution

It introduces a novel analysis of Jeans instability incorporating dissipation within the BGK framework without the Jeans swindle.

Findings

Perturbations larger than Jeans wavelength grow over time.

Dissipation reduces the growth rate of density contrast.

Perturbations smaller than Jeans wavelength oscillate and these oscillations fade due to dissipation.

Abstract

Jeans instability is analysed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a space-time Newtonian gravitational potential which satisfy the BGK model of the Boltzmann and Poisson equations without the necessity to invoke "Jeans swindle". The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation.