Methods for studying the accuracy of light propagation in N-body simulations

Abstract

It is proposed to use exact, cosmologically relevant solutions to Einstein's equations to accurately quantify the precision of ray tracing techniques through Newtonian N-body simulations. As an initial example of such a study, the recipe in (Green & Wald, 2012) for going between N-body results and a perturbed FLRW metric in the Newtonian gauge is used to study light propagation through quasi-spherical Szekeres models. The study is conducted by deriving a set of ODEs giving an expression for the angular diameter distance in the Newtonian gauge metric. The accuracy of the results obtained from the ODEs is estimated by using the ODEs to determine the distance-redshift relation in mock N-body data based on quasi-spherical Szekeres models. The results are then compared to the exact relations. From this comparison it is seen that the obtained ODEs can accurately reproduce the distance-redshift relation along both radial and non-radial geodesics in spherically symmetric models. The reproduction of geodesics in non-symmetric Szekeres models is slightly less accurate, but still good. These results indicate that the employment of perturbed FLRW metrics for standard ray tracing techniques yields fairly accurate results, at least regarding distance-redshift relations. It is possible though, that this conclusion will be rendered invalid if other typical ray tracing approximations are included and if light is allowed to travel through several structures instead of just one.

21 pages, 9 figures. Minor changes to match content of published version + one comment added (footnote 1) after publication. v3: Typos in equation 6 corrected

References in corpus (6)

• Luminosity distance in "Swiss cheese" cosmology with randomized voids: I. Single void size
• Applicability of the linearly perturbed FRW metric and Newtonian cosmology
• Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?
• LTB solutions in Newtonian gauge: from strong to weak fields
• Structure Formation, Backreaction and Weak Gravitational Fields
• Effect of inhomogeneities on high precision measurements of cosmological distances

Cited by in corpus (25)

• Differential cosmic expansion and the Hubble flow anisotropy
• Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
• Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results
• Multiple non-spherical structures from the extrema of Szekeres scalars
• Towards statistically homogeneous and isotropic perfect fluid universes with cosmic backreaction
• Studying the precision of ray tracing techniques with Szekeres models
• Redshift drift in an inhomogeneous universe: averaging and the backreaction conjecture
• Coarse-grained description of cosmic structure from Szekeres models
• Non-Spherical Szekeres models in the language of Cosmological Perturbations
• The Local Value of $H_0$ in an Inhomogeneous Universe
• Symmetry and Equivalence in Szekeres Models
• Cosmic backreaction and the mean redshift drift from symbolic regression
• Lagrangian theory of structure formation in relativistic cosmology. VI. Comparison with Szekeres exact solutions
• Frame Rotation in the Szekeres Spacetimes
• Exact Geodesic Distances in FLRW Spacetimes
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• On general-relativistic Lagrangian perturbation theory and its non-perturbative generalization
• Magrathea-Pathfinder: A 3D adaptive-mesh code for geodesic ray tracing in $N$-body simulations
• Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities
• Hubble Diagrams in Statistically Homogeneous, Anisotropic Universes
• Testing inhomogeneous cosmography in our cosmic neighborhood using CosmicFlows-4
• Beyond relativistic Lagrangian perturbation theory. I. An exact-solution controlled model for structure formation
• Accurately computing weak lensing convergence
• Direct correspondence between Newtonian gravitation and general relativity
• High Performance Algorithms for Quantum Gravity and Cosmology