# A cosmologically motivated reference formulation of numerical relativity

## TL;DR

This paper introduces a new reference formulation of Einstein's equations for numerical relativity in cosmology, reducing errors significantly by evolving differences from a reference solution, thus improving simulation accuracy and efficiency.

## Contribution

The paper proposes a novel reference formulation that evolves differences from a reference solution, enhancing accuracy in cosmological numerical relativity simulations.

## Key findings

- Error reduction by an order of magnitude or more
- Performance depends on the quality of the reference solution
- Potential for more accurate and efficient cosmological simulations

## 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.