# Comparing fully general relativistic and Newtonian calculations of structure formation

## Abstract

In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, in this paper we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. Finally, they only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.

- Authors:

- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology; Univ. of Copenhagen (Denmark). Niels Bohr Inst. Dark Cosmology Centre
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology

- Publication Date:

- Research Org.:
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Univ. of Copenhagen (Denmark); SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE; Innovation, Science and Economic Development Canada (ISED); Ministry of Research, Innovation and Science of Ontario (Canada); Villum Foundation (Denmark)

- OSTI Identifier:
- 1423562

- Grant/Contract Number:
- AC02-76SF00515; 16599

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; general relativity; large scale structure of the universe; relativistic aspects of cosmology; astrophysical & cosmological simulations; numerical relativity

### Citation Formats

```
East, William E., Wojtak, Radosław, and Abel, Tom.
```*Comparing fully general relativistic and Newtonian calculations of structure formation*. United States: N. p., 2018.
Web. doi:10.1103/physrevd.97.043509.

```
East, William E., Wojtak, Radosław, & Abel, Tom.
```*Comparing fully general relativistic and Newtonian calculations of structure formation*. United States. doi:10.1103/physrevd.97.043509.

```
East, William E., Wojtak, Radosław, and Abel, Tom. Tue .
"Comparing fully general relativistic and Newtonian calculations of structure formation". United States.
doi:10.1103/physrevd.97.043509.
```

```
@article{osti_1423562,
```

title = {Comparing fully general relativistic and Newtonian calculations of structure formation},

author = {East, William E. and Wojtak, Radosław and Abel, Tom},

abstractNote = {In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, in this paper we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. Finally, they only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.},

doi = {10.1103/physrevd.97.043509},

journal = {Physical Review D},

number = 4,

volume = 97,

place = {United States},

year = {Tue Feb 13 00:00:00 EST 2018},

month = {Tue Feb 13 00:00:00 EST 2018}

}

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