# Relic neutrino decoupling with flavour oscillations revisited

## Abstract

We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, N{sub eff}. We find a value of N{sub eff}=3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that N{sub eff} can be reduced down to 3.040 or enhanced up to 3.059.

- Authors:

- Instituto de Física Corpuscular (CSIC-Universitat de València),Parc Científic UV, C/ Catedrático José Beltrán 2, E-46980 Paterna (Valencia) (Spain)
- (TTK),RWTH Aachen University, D-52056 Aachen (Germany)

- Publication Date:

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

- OSTI Identifier:
- 22572124

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 07; Other Information: PUBLISHER-ID: JCAP07(2016)051; OAI: oai:repo.scoap3.org:16593; cc-by 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; COLLISION INTEGRALS; COSMOLOGY; DECOUPLING; DENSITY MATRIX; ENERGY DENSITY; FLAVOR MODEL; KINETIC EQUATIONS; NEUTRINO OSCILLATION; NEUTRINO-ELECTRON INTERACTIONS; NEUTRINOS; REST MASS; SPACE VEHICLES; UNIVERSE

### Citation Formats

```
Salas, Pablo F. de, Institute for Theoretical Particle Physics and Cosmology, and Pastor, Sergio.
```*Relic neutrino decoupling with flavour oscillations revisited*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/07/051.

```
Salas, Pablo F. de, Institute for Theoretical Particle Physics and Cosmology, & Pastor, Sergio.
```*Relic neutrino decoupling with flavour oscillations revisited*. United States. doi:10.1088/1475-7516/2016/07/051.

```
Salas, Pablo F. de, Institute for Theoretical Particle Physics and Cosmology, and Pastor, Sergio. Thu .
"Relic neutrino decoupling with flavour oscillations revisited". United States.
doi:10.1088/1475-7516/2016/07/051.
```

```
@article{osti_22572124,
```

title = {Relic neutrino decoupling with flavour oscillations revisited},

author = {Salas, Pablo F. de and Institute for Theoretical Particle Physics and Cosmology and Pastor, Sergio},

abstractNote = {We study the decoupling process of neutrinos in the early universe in the presence of three-flavour oscillations. The evolution of the neutrino spectra is found by solving the corresponding momentum-dependent kinetic equations for the neutrino density matrix, including for the first time the proper collision integrals for both diagonal and off-diagonal elements. This improved calculation modifies the evolution of the off-diagonal elements of the neutrino density matrix and changes the deviation from equilibrium of the frozen neutrino spectra. However, it does not vary the contribution of neutrinos to the cosmological energy density in the form of radiation, usually expressed in terms of the effective number of neutrinos, N{sub eff}. We find a value of N{sub eff}=3.045, in agreement with previous theoretical calculations and consistent with the latest analysis of Planck data. This result does not depend on the ordering of neutrino masses. We also consider the effect of non-standard neutrino-electron interactions (NSI), predicted in many theoretical models where neutrinos acquire mass. For two sets of NSI parameters allowed by present data, we find that N{sub eff} can be reduced down to 3.040 or enhanced up to 3.059.},

doi = {10.1088/1475-7516/2016/07/051},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 07,

volume = 2016,

place = {United States},

year = {Thu Jul 28 00:00:00 EDT 2016},

month = {Thu Jul 28 00:00:00 EDT 2016}

}