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Title: 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 » ν) 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(Σm ν), 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.« less

Authors:
 [1];  [2];  [1]; ORCiD logo [3]
  1. Univ. of Chicago, Chicago, IL (United States)
  2. Univ. of Chicago, Chicago, IL (United States); Leiden Univ., Leiden (The Netherlands)
  3. Carnegie Mellon Univ., Pittsburgh, PA (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Kavli Foundation; National Aeronautic and Space Administration (NASA); National Science Foundation (NSF)
OSTI Identifier:
1413677
Alternate Identifier(s):
OSTI ID: 1420363; OSTI ID: 1594047
Report Number(s):
FERMILAB-PUB-17-572-A; arXiv:1711.08434
Journal ID: ISSN 2470-0010; PRVDAQ; 1637562
Grant/Contract Number:  
AC02-07CH11359; PHY-1125897; FG02-13ER41958; NNX15AK22G; 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; Cosmological parameters; Cosmology; Large scale structure of the Universe; Neutrinos; Mass; Bayesian methods; Random matrix theory

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. https://www.osti.gov/servlets/purl/1413677.
@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},
issn = {2470-0010},
number = 4,
volume = 97,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 12 works
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Figures / Tables:

FIG. 1 FIG. 1: Ad hoc choices for the prior probability on Σmν.

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