A cosmologically motivated reference formulation of numerical relativity

Abstract

The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as possible, we investigate a novel formulation of Einstein's equations. This formulation evolves differences from a "reference" solution describing the dominant behavior of the spacetime, which mitigates error due to both truncation and approximate finite difference calculations. We find that the error in solutions obtained using the reference formulation can be smaller by an order of magnitude or more, with the level of improvement depending on how well the reference solution approximates the exact solution.

15 pages, 5 figures, planning to submit to CQG

References in corpus (7)

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Cited by in corpus (14)

• Einstein's Universe: Cosmological structure formation in numerical relativity
• Preheating in Full General Relativity
• Safely smoothing spacetime: backreaction in relativistic cosmological simulations
• The trouble with Hubble: Local versus global expansion rates in inhomogeneous cosmological simulations with numerical relativity
• Relativistic wide-angle galaxy bispectrum on the light-cone
• GRAMSES: a new route to general relativistic $N$-body simulations in cosmology. Part I. Methodology and code description
• The Limited Accuracy of Linearized Gravity
• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Backreaction and FRW consistency conditions
• General Relativistic Cosmological N-body Simulations I: time integration
• Cosmology using numerical relativity
• fNL - gNL mixing in the matter density field at higher orders
• Evaluating backreaction with the ellipsoidal collapse model
• Does relativistic cosmology software handle emergent volume evolution?