Perturbing Friedmann equations: an introduction to Lifshitz instability

Details Perturbing Friedmann equations: an introduction to Lifshitz instability Perturbing Friedmann equations: an introduction to Lifshitz instability

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...420..512h&link_type=abstract

The Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 420, no. 2, p. 512-524

Mathematics

Logic

10

Cosmology, Heuristic Methods, Newton Methods, Perturbation Theory, Equations Of State, Gauge Invariance, Poisson Equation, Scalars, Space-Time Functions

Scientific paper

A heuristic way of performing an analysis of cosmological perturbations by perturbing the Friedmann-Lemaitre-Robertson-Walker (FLRW) background equations is shown to be fully justified. This is possible because the Friedmann equation is valid even to perturbed order in general and the FLRW equations are valid to linear order in a pressureless medium. The existence of a curvature variable that remains constant, to linear order, on large scales is also useful in creating a simple description. A complete analysis which is analogous to the heuristic method, and to a more accessible Newtonian analysis, is also presented. Thus, recent and important results in this field can be explained in simple ways without any loss of rigor. One such result is the existence of conserved quantities which allow a simple connection between large-scale linear structure at present and conditions in the early universe. The conservation of the curvature variable in the large-scale limit, together with the validity of the Friedmann equation to linear order, implies a Friedmann-like evolution of a large scale perturbed region of the universe. We also give a practical way of understanding the generation and evolution of large-scale structures in the universe. This presentation provides an introduction to the specialized field of gravitational instability in an expanding universe, i.e., the Lifshitz instability.

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