Why there is no Newtonian backreaction

Abstract

In the conventional framework for cosmological dynamics the scale factor a(t) is assumed to obey the 'background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of a(t) viaNewtonian (or 'kinematic') backreaction and that this may avoid the need for dark energy. Here we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for a(t). The recently proposed modification of Racz et al. (2017) does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the 'generalised Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's Q tends very rapidly to zero for large volume and that this does not simply arise 'by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-z universe, there is no backreaction of structure on a(t) and that the need for dark energy cannot be avoided in this way.

Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

“…The negligible impact of inhomogeneities on the global evolution and observational parameters of cosmological models is supported by general considerations concerning the backreaction effect [26][27][28][29][30][31] and perturbative analysis of weak gravitational lensing [32]. However, these approaches are often criticized as incomplete or inconclusive because of restrictive assumptions made [33][34][35][36].…”

Einstein’s Universe: Cosmological structure formation in numerical relativity

“…Global averages Figure 6 shows the global evolution of the effective scale factor, a D . The blue curve shows a D calculated over the whole L = 1 Gpc, 256 3 resolution domain with (31). The purple dashed curve in the top panel shows the corresponding FLRW solution for the scale factor, a FLRW , found by solving the Hamiltonian constraint for a flat, matter-dominated, homogeneous, isotropic Universe in the longitudinal gauge,…”

“…Additional "backreaction" terms exist, but their significance has been debated [e.g. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

On Backreaction in Newtonian cosmology

“…We conclude that there is no new result in Kaiser (2017b). Known for twenty years, the result of is key to Newtonian cosmology, and is uncontroversial among researchers working on backreaction problems.…”

“…In a recent paper Kaiser (2017b; hereafter K17) considers, as do hereafter BE-see also the Euler-Poisson system in the fluid approximation for a "dust" matter model in the mean field approximation of Newtonian gravity, Eqs. ( 2) and (3) in K17 (cf.…”