Quasi-Newtonian dust cosmologies

TL;DR

This paper develops a quasi-Newtonian framework for dust cosmologies, revealing that consistency issues arise at the first derivative level, but can be addressed through linearization around FLRW backgrounds with additional source terms.

Contribution

It introduces a novel quasi-Newtonian formulation for dust cosmologies and demonstrates how to achieve self-consistency via linearization, accounting for peculiar motions.

Findings

Consistency at first derivative level is not achieved without linearization.

Linearization around FLRW backgrounds yields additional source terms.

The approach accounts for non-relativistic peculiar motions in density fluctuations.

Abstract

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = \alpha \Theta N$ ($\alpha = {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.