# Higher-order massive neutrino perturbations in large-scale structure

## Abstract

We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlasov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at ∼< 1% accuracy, we find that the total matter bispectrum with a low neutrino mass m = 0.046 eV can be reproduced by all but the fluid approximation, whilemore »

- Authors:

- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
- School of Physics, The University of New South Wales, Sydney NSW 2052 (Australia)

- Publication Date:

- OSTI Identifier:
- 22525924

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; APPROXIMATIONS; BENCHMARKS; BOLTZMANN-VLASOV EQUATION; CORRECTIONS; COSMIC NEUTRINOS; DENSITY; DISTURBANCES; FLUIDS; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; PHASE SPACE; REST MASS

### Citation Formats

```
Führer, Florian, and Wong, Yvonne Y.Y., E-mail: fuehrer@thpys.uni-heidelberg.de, E-mail: yvonne.y.wong@unsw.edu.au.
```*Higher-order massive neutrino perturbations in large-scale structure*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/03/046.

```
Führer, Florian, & Wong, Yvonne Y.Y., E-mail: fuehrer@thpys.uni-heidelberg.de, E-mail: yvonne.y.wong@unsw.edu.au.
```*Higher-order massive neutrino perturbations in large-scale structure*. United States. doi:10.1088/1475-7516/2015/03/046.

```
Führer, Florian, and Wong, Yvonne Y.Y., E-mail: fuehrer@thpys.uni-heidelberg.de, E-mail: yvonne.y.wong@unsw.edu.au. Sun .
"Higher-order massive neutrino perturbations in large-scale structure". United States.
doi:10.1088/1475-7516/2015/03/046.
```

```
@article{osti_22525924,
```

title = {Higher-order massive neutrino perturbations in large-scale structure},

author = {Führer, Florian and Wong, Yvonne Y.Y., E-mail: fuehrer@thpys.uni-heidelberg.de, E-mail: yvonne.y.wong@unsw.edu.au},

abstractNote = {We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlasov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at ∼< 1% accuracy, we find that the total matter bispectrum with a low neutrino mass m = 0.046 eV can be reproduced by all but the fluid approximation, while for larger neutrino masses m=0.46 → 0.93 eV only the hybrid approach has the desired accuracy on a large range of scales. This result serves as a cautionary note that approximate nonlinear models of neutrino clustering that reproduce the gross features of some observables may not suffice for precision calculations, nor are they guaranteed to apply to other observables. All of the approximation schemes fail to reproduce the bispectrum of the neutrino density perturbations at better than 20% accuracy across all scales, indicating that an exact treatment of nonlinear neutrino perturbations is necessary.},

doi = {10.1088/1475-7516/2015/03/046},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2015,

place = {United States},

year = {Sun Mar 01 00:00:00 EST 2015},

month = {Sun Mar 01 00:00:00 EST 2015}

}