# Validity of the Born approximation for beyond Gaussian weak lensing observables

## Abstract

Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ ^{3}) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ ^{4}) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools softwaremore »

- Authors:

- Columbia Univ., New York, NY (United States). Dept. of Physics; Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Physics
- Columbia Univ., New York, NY (United States). Dept. of Astronomy; New York Univ. (NYU), NY (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF)

- OSTI Identifier:
- 1362165

- Alternate Identifier(s):
- OSTI ID: 1361575

- Report Number(s):
- BNL-113928-2017-JA

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0012704; ACI-1053575; AST-1210877

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 95; Journal Issue: 12; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Weak gravitational lensing; Simulations; Methods numerical, analytical, statistical

### Citation Formats

```
Petri, Andrea, Haiman, Zoltan, and May, Morgan.
```*Validity of the Born approximation for beyond Gaussian weak lensing observables*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.95.123503.

```
Petri, Andrea, Haiman, Zoltan, & May, Morgan.
```*Validity of the Born approximation for beyond Gaussian weak lensing observables*. United States. doi:10.1103/PhysRevD.95.123503.

```
Petri, Andrea, Haiman, Zoltan, and May, Morgan. Tue .
"Validity of the Born approximation for beyond Gaussian weak lensing observables". United States.
doi:10.1103/PhysRevD.95.123503. https://www.osti.gov/servlets/purl/1362165.
```

```
@article{osti_1362165,
```

title = {Validity of the Born approximation for beyond Gaussian weak lensing observables},

author = {Petri, Andrea and Haiman, Zoltan and May, Morgan},

abstractNote = {Accurate forward modeling of weak lensing (WL) observables from cosmological parameters is necessary for upcoming galaxy surveys. Because WL probes structures in the nonlinear regime, analytical forward modeling is very challenging, if not impossible. Numerical simulations of WL features rely on ray tracing through the outputs of N-body simulations, which requires knowledge of the gravitational potential and accurate solvers for light ray trajectories. A less accurate procedure, based on the Born approximation, only requires knowledge of the density field, and can be implemented more efficiently and at a lower computational cost. In this work, we use simulations to show that deviations of the Born-approximated convergence power spectrum, skewness and kurtosis from their fully ray-traced counterparts are consistent with the smallest nontrivial O(Φ3) post-Born corrections (so-called geodesic and lens-lens terms). Our results imply a cancellation among the larger O(Φ4) (and higher order) terms, consistent with previous analytic work. We also find that cosmological parameter bias induced by the Born-approximated power spectrum is negligible even for a LSST-like survey, once galaxy shape noise is considered. When considering higher order statistics such as the κ skewness and kurtosis, however, we find significant bias of up to 2.5σ. Using the LensTools software suite, we show that the Born approximation saves a factor of 4 in computing time with respect to the full ray tracing in reconstructing the convergence.},

doi = {10.1103/PhysRevD.95.123503},

journal = {Physical Review D},

number = 12,

volume = 95,

place = {United States},

year = {Tue Jun 06 00:00:00 EDT 2017},

month = {Tue Jun 06 00:00:00 EDT 2017}

}

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