Do Newtonian large-scale structure simulations fail to include relativistic effects?

Abstract

The Newtonian simulations describing the formation of large-scale structures do not include relativistic effects. A new approach to this problem is proposed, which consists of splitting the HawkingHayward quasi-local energy of a closed spacelike 2-surface into a "Newtonian" part due to local perturbations and a "relativistic" part due to the cosmology. It is found that the Newtonian part dominates over the relativistic one as time evolves, lending support to the validity of Newtonian simulations.PACS numbers: 98.62.Py, 98.80.Jk

Turnaround size of non-spherical structures

“…Correspondingly, the Poisson equation (which can be obtained as the Newtonian approximation of the Einstein equations for the post-Newtonian geometry [23])…”

“…In this gauge, the line element is explicitly conformal to the post-Newtonian geometry (2). The Hawking-Hayward mass M HH contained in a topological 2-sphere S in the spacetime (23) was computed in Ref. [23] in two ways.…”

“…The Hawking-Hayward mass M HH contained in a topological 2-sphere S in the spacetime (23) was computed in Ref. [23] in two ways. The first method employs the transformation property of the Hawking-Hayward quasi-local mass under the conformal transformation of the spacetime metric g ab →g ab = Ω 2 g ab .…”

“…Working, for simplicity, in the framework of GR and limiting ourselves to the first order in the metric perturbations of a spatially flat FLRW universe dominated by a single dark energy fluid (such that w ≡ p/ρ ≈ −1) and restricting to spherically symmetric perturbations, the Hawking-Hayward quasi-local mass (which reduces to the Misner-Sharp-Hernandez mass [21,22] in the spherical case) is computed for a spherical surfaceS containing all contributions due to the local perturbations. This quasi-local mass can be split into two contributions [23], namelyM…”

“…(1) as the contribution due to the energy of the local perturbation, whereas the second term is due to the cosmological expansion. Hence, a natural definition of turnaround radius is obtained by requiring these two terms to be equal [23]. The turnaround radius has been discussed also in alternative theories of gravity (see e.g.…”