Neutrino mass priors for cosmology from random matrices
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 basisinvariant 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:

^{[1]};
^{[2]};
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^{[3]}
 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:
 Report Number(s):
 FERMILABPUB17572A; arXiv:1711.08434
Journal ID: ISSN 24700010; PRVDAQ; 1637562
 Grant/Contract Number:
 AC0207CH11359; FG0213ER41958; SC0009924
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1413677
 Alternate Identifier(s):
 OSTI ID: 1420363
Long, Andrew J., Raveri, Marco, Hu, Wayne, and Dodelson, Scott. Neutrino mass priors for cosmology from random matrices. United States: N. p.,
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. 2018.
"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 basisinvariant 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 = {2018},
month = {2}
}