Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions

Abstract

In this work we present the first results from a new ray-tracing tool to calculate cosmological distances in the context of fully nonlinear general relativity. We use this tool to study the ability of the general cosmographic representation of luminosity distance, as truncated at third order in redshift, to accurately capture anisotropies in the “true” luminosity distance. We use numerical relativity simulations of cosmological large-scale structure formation which are free from common simplifying assumptions in cosmology. We find the general, third-order cosmography is accurate to within 1% for redshifts to z ≈ 0.034 when sampling scales strictly above 100 h -1 Mpc, which is in agreement with an earlier prediction. We find the inclusion of small-scale structure generally spoils the ability of the third-order cosmography to accurately reproduce the full luminosity distance for wide redshift intervals, as might be expected. For a simulation sampling small-scale structures, we find a ∼ ±5% variance in the monopole of the ray-traced luminosity distance at z ≈ 0.02. Further, all 25 observers we study here see a 9–20% variance in the luminosity distance across their sky at z ≈ 0.03, which reduces to 2–5% by z ≈ 0.1. These calculations are based on simulations and ray tracing which adopt fully nonlinear general relativity, and highlight the potential importance of fair sky-sampling in low-redshift isotropic cosmological analysis.

Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study

“…In a general inhomogeneous universe, we naturally expect anisotropies in cosmological parameters due to structures nearby the observer (Heinesen 2021, and references therein). Such anisotropies reduce as we approach the homogeneity scale, however, they have been shown to potentially remain significant up to z ≈ 0.1 (Macpherson 2023). Anisotropic variance in cosmological parameters could bias low-redshift measurements using data that does not fairly sample the whole sky.…”

“…However, the authors used unrealistic sky-samplings as well as approximate distances from a Taylor series expansion truncated at third order in redshift. This level of truncation was subsequently shown to give distances incorrect at the ∼ 10% level at z ≈ 0.1 (Macpherson 2023).…”

EBWeyl: a code to invariantly characterize numerical spacetimes

“…Both the scalar invariants of the previous section and the gauge-invariant perturbations discussed above are local quantities, but in cosmology observers cannot go in a galaxy far away and measure E µν{u} and B µν{u} there: rather we have to link points (spacetime events) on the past light-cone of the observer, points where local observables are defined, with the point of the observers themselves, i.e. ray tracing is key, see [32] for a concrete example in numerical relativistic cosmology and an application to simulation comparisons and [14,[129][130][131] and references therein for a general discussion. Nonetheless, although the issue of defining observables is simple for first-order perturbations but more involved at second and higher-order, first-order gauge invariance, i.e.…”

“…Even in the general case, therefore, coordinates or frame transformations can be used to make four of these ten components vanish, or two complex Weyl scalars. 14 In analogy to the relation between the Newtonian gravitational potential and the Newtonian tidal field.…”

“…Enabled and motivated by new computational resources and observational advances, numerical relativity simulations as an alternative to Newtonian simulations have been gaining interest in cosmology in recent years, some in full general relativity using a fluid description of matter [1,2,[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], some using a particle description [18][19][20][21][22][23]; approximation are used in certain cases, such as weak field or neglecting transverse-traceless tensor modes, on the assumption that they represent gravitational waves uninfluential for the dynamics. This has been pushing our understanding of the significance of relativistic effects on cosmological scales [9,[22][23][24][25][26].…”