2012/03/31 by Cornelius Rampf, Thomas Buchert · 1 citation
Physics and Astronomy · #astro-ph.CO
paper · pdf · doi:10.1088/1475-7516/2012/06/021
published as JCAP06 (2012) 021 · 31 pages, matches published version in JCAP, added an extra section which discusses and motivates the choice of initial conditions, extended the title for the sake of precision
arxiv created 2012/06/14 · arxiv updated 2012/06/15
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions---both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.