Second order cosmological perturbations: a minimal approach

Details Second order cosmological perturbations: a minimal approach Second order cosmological perturbations: a minimal approach

2012-03-21

arxiv.org/abs/1203.4790v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

29 pages, no figures

Scientific paper

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann-Lemaitre cosmologies, whose equations are notoriously complicated. Our goal in this paper is to derive the governing equations for second order perturbations of Friedmann-Lemaitre cosmologies in gauge-invariant form in a way that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress-energy tensor. We specialize our general equations to two gauges, the Poisson gauge and the uniform curvature gauge, obtaining equations that are significantly simpler than those in the literature when comparisons can be made, due firstly to our choice of variables, and secondly to our use of differential operators and mode extraction operators.

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