Quasi-Newtonian dust cosmologies

Details Quasi-Newtonian dust cosmologies Quasi-Newtonian dust cosmologies

1998-05-22

arxiv.org/abs/gr-qc/9805087v2

Class.Quant.Grav. 15 (1998) 3545-3573

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, LaTeX 2.09 (10pt), to appear in Classical and Quantum Gravity, Vol. 15 (1998)

Scientific paper

10.1088/0264-9381/15/11/017

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.

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