What question did this study set out to answer?

The study aims to evaluate the numerical consistency of effective backreaction models in cosmology.

May 19, 20260 citationsOpen Access

Numerical Relativistic Cosmology: Effective Backreaction Models and BSSN Comparison

Key Points

The study aims to evaluate the numerical consistency of effective backreaction models in cosmology.
Implemented BSSN formulation within the Einstein Toolkit for full 3+1 numerical relativity.
Utilized Buchert scalar averaging formalism and GPU-accelerated simulations for effective backreaction.
Performed comparative analysis with various resolutions (128³, 256³, 512³) and statistical methods.
Stable BSSN ensemble backreaction measured as Q_D = (1.536 ± 0.014) × 10⁻⁴.
Effective model showed convergence across all tested resolutions with a calibration factor Z ≈ 5.47 × 10³.
Pantheon+ comparison yielded Δχ² = −8.0, indicating no statistically significant improvement over flat ΛCDM.

Abstract

This repository contains the numerical and analysis framework accompanying the study: “Numerical Relativistic Cosmology: Effective Backreaction Models and BSSN Comparison” The project presents a comparative investigation of cosmological backreaction across three complementary approaches: • Full 3+1 numerical relativity using the BSSN formulation implemented in the Einstein Toolkit• Buchert scalar averaging formalism• GPU-accelerated phenomenological effective backreaction simulations inspired by Buchert averaging The work focuses on numerical consistency between effective averaging approaches and weakly perturbed full-GR evolutions rather than proposing a replacement for dark energy. Included in this repository: GPU simulation codes for effective backreaction evolution Numerical convergence datasets (128³, 256³, 512³ resolutions) BSSN ensemble analysis outputs Pantheon+ Type Ia supernova likelihood comparison scripts Data products used to generate figures and tables in the manuscript Key results: Stable BSSN ensemble backreaction: QD = (1. 536 ± 0. 014) × 10⁻⁴ GPU effective model convergence across all tested resolutions Empirical calibration factor: Z ≈ 5. 47 × 10³used to map effective amplitudes to BSSN-derived backreaction values Pantheon+ comparison: χ² = 827. 2 for the effective model versus χ² = 835. 2 for flat ΛCDM The improvement Δχ² = −8. 0 is not statistically significant Important note: The GPU effective model is phenomenological and does NOT constitute a direct numerical solution of Einstein’s equations. The calibration factor Z is setup-dependent and should not be interpreted as a universal physical constant. The present study should therefore be interpreted as a reproducible numerical comparison framework between effective cosmological averaging models and weakly perturbed general-relativistic simulations. Hardware and software: Einstein Toolkit (Cactus + MLBSSN + Carpet) CUDA 13. 0 NVIDIA GTX 1080 Ti MPI parallelization Grid resolutions up to 512³ cells Potential applications: Numerical relativity in cosmology Backreaction studies Effective averaging methods GPU cosmological simulations Phenomenological large-scale structure modeling Citation: If you use this repository, please cite the associated paper and Zenodo record. Author: Alexander TikhonovIndependent Researcher2026

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