# Neutrino mass priors for cosmology from random matrices

## Abstract

Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, Σm _{ν}, through Bayesian inference. Because these constraints depend on the choice for the prior probability π(Σm _{ν}), we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature. The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix M _{ν}, since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over M _{ν}, and by including the known squared mass splittings, we predict a theoretical probability distribution over Σm _{ν} that we interpret as a Bayesian prior probability π(Σm _{ν}). Assuming a basis-invariant probability distribution on M _{ν}, also known as the anarchy hypothesis, we find that π(Σm _{ν}) peaks close to the smallest Σm _{ν} allowed by the measured mass splittings, roughly 0.06 eV (0.1 eV) for normal (inverted) ordering, due to the phenomenon of eigenvalue repulsion in random matrices. We consider three models for neutrino mass generation: Dirac, Majorana, and Majorana via the seesaw mechanism; differences in the predicted priors π(Σmmore »

- Authors:

- Univ. of Chicago, Chicago, IL (United States)
- Univ. of Chicago, Chicago, IL (United States); Leiden Univ., Leiden (The Netherlands)
- Carnegie Mellon Univ., Pittsburgh, PA (United States)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

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

- OSTI Identifier:
- 1413677

- Alternate Identifier(s):
- OSTI ID: 1420363

- Report Number(s):
- FERMILAB-PUB-17-572-A; arXiv:1711.08434

Journal ID: ISSN 2470-0010; PRVDAQ; 1637562

- Grant/Contract Number:
- AC02-07CH11359; FG02-13ER41958; SC0009924

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Long, Andrew J., Raveri, Marco, Hu, Wayne, and Dodelson, Scott.
```*Neutrino mass priors for cosmology from random matrices*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.043510.

```
Long, Andrew J., Raveri, Marco, Hu, Wayne, & Dodelson, Scott.
```*Neutrino mass priors for cosmology from random matrices*. United States. doi:10.1103/PhysRevD.97.043510.

```
Long, Andrew J., Raveri, Marco, Hu, Wayne, and Dodelson, Scott. Tue .
"Neutrino mass priors for cosmology from random matrices". United States.
doi:10.1103/PhysRevD.97.043510.
```

```
@article{osti_1413677,
```

title = {Neutrino mass priors for cosmology from random matrices},

author = {Long, Andrew J. and Raveri, Marco and Hu, Wayne and Dodelson, Scott},

abstractNote = {Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses, Σmν, through Bayesian inference. Because these constraints depend on the choice for the prior probability π(Σmν), we argue that this prior should be motivated by fundamental physical principles rather than the ad hoc choices that are common in the literature. The first step in this direction is to specify the prior directly at the level of the neutrino mass matrix Mν, since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over Mν, and by including the known squared mass splittings, we predict a theoretical probability distribution over Σmν that we interpret as a Bayesian prior probability π(Σmν). Assuming a basis-invariant probability distribution on Mν, also known as the anarchy hypothesis, we find that π(Σmν) peaks close to the smallest Σmν allowed by the measured mass splittings, roughly 0.06 eV (0.1 eV) for normal (inverted) ordering, due to the phenomenon of eigenvalue repulsion in random matrices. We consider three models for neutrino mass generation: Dirac, Majorana, and Majorana via the seesaw mechanism; differences in the predicted priors π(Σmν) allow for the possibility of having indications about the physical origin of neutrino masses once sufficient experimental sensitivity is achieved. In conclusion, we present fitting functions for π(Σmν), which provide a simple means for applying these priors to cosmological constraints on the neutrino masses or marginalizing over their impact on other cosmological parameters.},

doi = {10.1103/PhysRevD.97.043510},

journal = {Physical Review D},

number = 4,

volume = 97,

place = {United States},

year = {Tue Feb 13 00:00:00 EST 2018},

month = {Tue Feb 13 00:00:00 EST 2018}

}

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