In this paper the authors introduce a new way of expressing the relativistic density contrast of matter perturbations in four commonly used gauges, both at first and second orders.
This new method is very interesting, since it provides a unified treatment of the density contrast in the various gauges, thus allowing a straightforward comparison of results obtained by other authors in different gauges. This should be useful when computing non-trivial effects such as the properties of primordial non-Gaussianities in the large scale structure, but also when assessing the correspondence between Newtonian and relativistic perturbations, an important topic in order to interpret adequately the results of N-body simulations.
To achieve this remarkable unification, the authors restrict their analysis to a flat Friedmann-Lemaitre-Robertson-Walker background in the presence of dust and a cosmological constant. Then, they use the comoving curvature perturbation to describe the spatial dependence of the density contrast, and identify a set of quadratic differential operators acting on this curvature perturbation. This allows them to physically organise the various terms in the expressions of the density contrast at second order in terms of a super-horizon part, a post-Newtonian part, and a Newtonian part. As expected, the Newtonian part does not depend on the gauge, whereas the two other parts do depend on it, but retain the same functional forms. This ordering of the terms in the expression for the density contrast then allows the authors to compare the results in the various gauges and to study some asymptotic properties of the density contrast.
Read the full article in Classical and Quantum Gravity:
Simple expressions for second order density perturbations in standard cosmology
Claes Uggla and John Wainwright
Class. Quantum Grav. 31 105008
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