Cosmological Perturbation Theory and the Evolution of Small-Scale Inhomogeneities

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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22 pages, 1 figure. Presentation much improved. Article is self-contained. Section on classical standard evolution equation re

Scientific paper

It is shown that a first-order cosmological perturbation theory for the open, flat and closed Friedmann-Lemaitre-Robertson-Walker universes admits one, and only one, gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual Newtonian energy density in the non-relativistic limit. The same holds true for the perturbation to the particle number density. Using these two new variables, a new manifestly covariant and gauge-invariant cosmological perturbation theory based on the Lifshitz-Khalatnikov theory has been developed. Perturbations in the total energy density are gravitationally coupled to perturbations in the particle number density, irrespective of the nature of the particles. There is, in first-order, no back-reaction of perturbations to the global expansion of the universe. Small-scale perturbations in the radiation-dominated era oscillate with an increasing amplitude. Density perturbations evolve diabatically, i.e., they exchange heat with their environment. This heat loss of a perturbation may enhance the growth rate of its mass sufficiently to explain stellar formation, a phenomenon not understood, as yet, without the additional assumption of the existence of Cold Dark Matter. This theoretical observation is the main result of this article.

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