# Active-sterile neutrino oscillations in the early Universe with full collision terms

## Abstract

Sterile neutrinos are thermalised in the early Universe via oscillations with the active neutrinos for certain mixing parameters. The most detailed calculation of this thermalisation process involves the solution of the momentum-dependent quantum kinetic equations, which track the evolution of the neutrino phase space distributions. Until now the collision terms in the quantum kinetic equations have always been approximated using equilibrium distributions, but this approximation has never been checked numerically. In this work we revisit the sterile neutrino thermalisation calculation using the full collision term, and compare the results with various existing approximations in the literature. We find a better agreement than would naively be expected, but also identify some issues with these approximations that have not been appreciated previously. These include an unphysical production of neutrinos via scattering and the importance of redistributing momentum through scattering, as well as details of Pauli blocking. Finally, we devise a new approximation scheme, which improves upon some of the shortcomings of previous schemes.

- Authors:

- Department of Physics and Astronomy,Aarhus University, 8000 Aarhus C (Denmark)
- (Denmark)
- (Australia)
- Institute of Cosmology and Gravitation, University of Portsmouth,Portsmouth PO1 3FX (United Kingdom)
- School of Physics, The University of New South Wales,Sydney NSW 2052 (Australia)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22458361

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 08; Other Information: PUBLISHER-ID: JCAP08(2015)019; OAI: oai:repo.scoap3.org:11373; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COLLISIONS; KINETIC EQUATIONS; MATHEMATICAL SOLUTIONS; NEUTRINO OSCILLATION; NEUTRINOS; PHASE SPACE; SCATTERING; UNIVERSE

### Citation Formats

```
Hannestad, Steen, Aarhus Institute of Advanced Studies,Aarhus University, 8000 Aarhus C, Hansen, Rasmus Sloth, School of Physics, The University of New South Wales,Sydney NSW 2052, Tram, Thomas, and Wong, Yvonne Y.Y.
```*Active-sterile neutrino oscillations in the early Universe with full collision terms*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/08/019.

```
Hannestad, Steen, Aarhus Institute of Advanced Studies,Aarhus University, 8000 Aarhus C, Hansen, Rasmus Sloth, School of Physics, The University of New South Wales,Sydney NSW 2052, Tram, Thomas, & Wong, Yvonne Y.Y.
```*Active-sterile neutrino oscillations in the early Universe with full collision terms*. United States. doi:10.1088/1475-7516/2015/08/019.

```
Hannestad, Steen, Aarhus Institute of Advanced Studies,Aarhus University, 8000 Aarhus C, Hansen, Rasmus Sloth, School of Physics, The University of New South Wales,Sydney NSW 2052, Tram, Thomas, and Wong, Yvonne Y.Y. Tue .
"Active-sterile neutrino oscillations in the early Universe with full collision terms". United States.
doi:10.1088/1475-7516/2015/08/019.
```

```
@article{osti_22458361,
```

title = {Active-sterile neutrino oscillations in the early Universe with full collision terms},

author = {Hannestad, Steen and Aarhus Institute of Advanced Studies,Aarhus University, 8000 Aarhus C and Hansen, Rasmus Sloth and School of Physics, The University of New South Wales,Sydney NSW 2052 and Tram, Thomas and Wong, Yvonne Y.Y.},

abstractNote = {Sterile neutrinos are thermalised in the early Universe via oscillations with the active neutrinos for certain mixing parameters. The most detailed calculation of this thermalisation process involves the solution of the momentum-dependent quantum kinetic equations, which track the evolution of the neutrino phase space distributions. Until now the collision terms in the quantum kinetic equations have always been approximated using equilibrium distributions, but this approximation has never been checked numerically. In this work we revisit the sterile neutrino thermalisation calculation using the full collision term, and compare the results with various existing approximations in the literature. We find a better agreement than would naively be expected, but also identify some issues with these approximations that have not been appreciated previously. These include an unphysical production of neutrinos via scattering and the importance of redistributing momentum through scattering, as well as details of Pauli blocking. Finally, we devise a new approximation scheme, which improves upon some of the shortcomings of previous schemes.},

doi = {10.1088/1475-7516/2015/08/019},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 08,

volume = 2015,

place = {United States},

year = {Tue Aug 11 00:00:00 EDT 2015},

month = {Tue Aug 11 00:00:00 EDT 2015}

}