Does relativistic cosmology software handle emergent volume evolution?
Abstract
Several software packages for relativistic cosmological simulations that do not fully implement the Einstein equation have recently been developed. Two of the freelicensed ones are INHOMOG and GEVOLUTION. A key question is whether globally emergent volume evolution that is faster than that of a Friedmannian reference model results from the averaged effects of structure formation. Checking that emergent volume evolution is correctly modelled by the packages is thus needed. We numerically replace the software's default random realisation of initial seed fluctuations by a fluctuation of spatially constant amplitude in a simulation's initial conditions. The average volume evolution of the perturbed model should follow that of a Friedmannian expansion history that corresponds to the original Friedmannian reference solution modified by the insertion of the spatially constant perturbation. We derive the equations that convert from the perturbed reference solution to the effective solution. We find that INHOMOG allows emergent volume evolution correctly at first order through to the current epoch. For initial conditions with a resolution of N = 128^{3} particles and an initial nonzero extrinsic curvature invariant I_{ i } = 0.001, INHOMOG matches an exact Friedmannian solution to 0.0058% (Einsteinde Sitter, EdS) or 0.0033% (ΛCDM). We find that GEVOLUTION models the decaying mode to fair accuracy, and excludes the growing mode by construction. For N = 128^{3} and an initial scalar potential Φ = 0.001, GEVOLUTION is accurate for the decaying mode to 0.012% (EdS) or 0.013% (ΛCDM). We conclude that this special case of an exact nonlinear solution for a perturbed Friedmannian model provides a robust calibration for relativistic cosmological simulations.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2022
 DOI:
 10.1088/13616382/ac8ddb
 arXiv:
 arXiv:2112.14174
 Bibcode:
 2022CQGra..39u5007B
 Keywords:

 methods: numerical;
 galaxies: evolution;
 cosmology: dark matter;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 v2: 34 pages, 6 figures, 2 tables