# Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals

## Abstract

Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional fast Fourier transform, which is significantly faster than the five-dimensional Monte-Carlo integrals that are needed otherwise. The general idea of this fast fourier transform perturbation theory method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Berkeley Center for Cosmological Physics, Dept. of Physics; Inst. for Advanced Study, Princeton, NJ (United States)
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics; Stanford Univ., CA (United States). Kavli Inst. for Particle Astrophysics and Cosmology; SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1360171

- Alternate Identifier(s):
- OSTI ID: 1333589

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 10; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Schmittfull, Marcel, and Vlah, Zvonimir.
```*Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.94.103530.

```
Schmittfull, Marcel, & Vlah, Zvonimir.
```*Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals*. United States. doi:10.1103/PhysRevD.94.103530.

```
Schmittfull, Marcel, and Vlah, Zvonimir. Mon .
"Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals". United States.
doi:10.1103/PhysRevD.94.103530. https://www.osti.gov/servlets/purl/1360171.
```

```
@article{osti_1360171,
```

title = {Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals},

author = {Schmittfull, Marcel and Vlah, Zvonimir},

abstractNote = {Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve this is to model nonlinear scales perturbatively. Unfortunately, this involves high-dimensional loop integrals that are cumbersome to evaluate. Here, trying to simplify this, we show how two-loop (next-to-next-to-leading order) corrections to the density power spectrum can be reduced to low-dimensional, radial integrals. Many of those can be evaluated with a one-dimensional fast Fourier transform, which is significantly faster than the five-dimensional Monte-Carlo integrals that are needed otherwise. The general idea of this fast fourier transform perturbation theory method is to switch between Fourier and position space to avoid convolutions and integrate over orientations, leaving only radial integrals. This reformulation is independent of the underlying shape of the initial linear density power spectrum and should easily accommodate features such as those from baryonic acoustic oscillations. We also discuss how to account for halo bias and redshift space distortions.},

doi = {10.1103/PhysRevD.94.103530},

journal = {Physical Review D},

number = 10,

volume = 94,

place = {United States},

year = {Mon Nov 28 00:00:00 EST 2016},

month = {Mon Nov 28 00:00:00 EST 2016}

}

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