Abstract
A number of codes for general-relativistic simulations of cosmological structure formation have been developed in recent years. Here we demonstrate that a sample of these codes produce consistent results beyond the Newtonian regime. We simulate solutions to Einstein’s equations dominated by gravitomagnetism—a vector-type gravitational field that does not exist in Newtonian gravity and produces frame-dragging, the leading-order post-Newtonian effect. We calculate the coordinate-invariant effect on intersecting null geodesics by performing ray tracing in each independent code. With this observable quantity, we assess and compare each code’s ability to compute relativistic effects.
Highlights
The flat Λ cold dark matter (ΛCDM) model is the backbone of modern cosmology
ΛCDM rests on three main pillars: (i) based on general relativity (GR) with a cosmological constant Λ, a Friedmann–Lemaître–Robertson–Walker (FLRW) metric is adopted as the description of the Universe on average, on the assumption of large-scale statistical homogeneity and isotropy; (ii) the relativistic perturbations of this background model are used to describe small inhomogeneities at large scales and early times, e.g. cosmic microwave background fluctuations; (iii) Newtonian dynamics is used to model structure formation at late times and on small scales, where nonlinearity in the matter distribution is important
Red circles show the results from gevolution, blue diamonds show the results from the Einstein Toolkit (ET), green squares show the results from CosmoGRaPH, and orange triangles show the results from gramses, with dashed lines showing the linear solution for reference
Summary
The flat Λ cold dark matter (ΛCDM) model is the backbone of modern cosmology. Originally proposed in the context of the inflationary scenario [1] and to accommodate for observations of structures on large scales [2], it has emerged as the concordance cosmological model [3, 4] after the discovery of the accelerating expansion of the Universe [5, 6]. A number of generalrelativistic codes with no assumed symmetries have been developed for cosmology, employing either a formally exact treatment of the metric [43,44,45,46,47,48,49] or an approximate scheme [50, 51] These tools provide new ways to study aspects of GR beyond the limited scope of known analytic solutions and perturbative expansions around them. They have been applied to quantify gravitational back-reaction of small-scale structures [52,53,54,55,56,57], light-cone projection effects [58,59,60,61], and the impact of relativistic species [62, 63] on the evolution and observation of large-scale structure.
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