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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, 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). We find that π(Σmν) peaks close to the smallest Σmν allowed by the measured mass splittings, roughly 0.06eV (0.1eV) 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. Wemore » 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.« less

Authors:
 [1];  [2];  [1]; ORCiD logo [3]
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  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); Carnegie Mellon Univ., Pittsburgh, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); Kavli Foundation; National Aeronautics and Space Administration (NASA); National Science Foundation (NSF)
OSTI Identifier:
1413677
Alternate Identifier(s):
OSTI ID: 1420363; OSTI ID: 1594047; OSTI ID: 1755503
Report Number(s):
FERMILAB-PUB-17-572-A; arXiv:1711.08434
Journal ID: ISSN 2470-0010; PRVDAQ; 1637562
Grant/Contract Number:  
SC0010118; AC02-07CH11359; PHY-1125897; FG02-13ER41958; NNX15AK22G; SC0009924
Resource Type:
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.
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Long, Andrew J., Raveri, Marco, Hu, Wayne, & Dodelson, Scott. Neutrino mass priors for cosmology from random matrices. United States. https://doi.org/10.1103/PhysRevD.97.043510
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Long, Andrew J., Raveri, Marco, Hu, Wayne, and Dodelson, Scott. Tue . "Neutrino mass priors for cosmology from random matrices". United States. https://doi.org/10.1103/PhysRevD.97.043510. https://www.osti.gov/servlets/purl/1413677.
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@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). We find that π(Σmν) peaks close to the smallest Σmν allowed by the measured mass splittings, roughly 0.06eV (0.1eV) 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. 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}
}
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Journal Article:
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https://doi.org/10.1103/PhysRevD.97.043510
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Cited by: 30 works
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Figures / Tables:

FIG. 1 FIG. 1: Ad hoc choices for the prior probability on Σmν.
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Works referenced in this record:

WiggleZ Dark Energy Survey: Cosmological neutrino mass constraint from blue high-redshift galaxies
journal, April 2012

Constraint on neutrino masses from SDSS-III/BOSS Lyα forest and other cosmological probes
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  • Palanque-Delabrouille, Nathalie; Yèche, Christophe; Lesgourgues, Julien
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X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue
journal, April 2014

μ→eγ at a rate of one out of 109 muon decays?
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Neutrino mixing and mass hierarchy in Gaussian landscapes
journal, January 2009

Neutrino mass and mixing: from theory to experiment
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journal, September 2016

Neutrino Mass Anarchy
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journal, April 2008

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Anarchy with hierarchy: A probabilistic appraisal
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Cosmological limits on neutrino unknowns versus low redshift priors
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Neutrino mass anarchy and the Universe
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Horizontal Symmetry and Masses of Neutrinos
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Unveiling ν secrets with cosmological data: Neutrino masses and mass hierarchy
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Neutrino mass limits: Robust information from the power spectrum of galaxy surveys
journal, September 2016

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
journal, September 2010

Bayesian comparison of U ( 1 ) lepton flavor models
journal, May 2014

Neutrino Mass and Spontaneous Parity Nonconservation
journal, April 1980

Neutrino masses in SU(2) ⊗ U(1) theories
journal, November 1980

Anarchy and neutrino physics
journal, April 2017

  • Fortin, Jean-François; Giasson, Nicolas; Marleau, Luc
  • Journal of High Energy Physics, Vol. 2017, Issue 4
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Cosmology and the neutrino mass ordering
journal, November 2016

Neutrino mixing anarchy: Alive and kicking
journal, July 2015

Impact of neutrino properties on the estimation of inflationary parameters from current and future observations
journal, February 2017

Neutrino masses and mixings: Status of known and unknown 3 ν parameters
journal, July 2016

Anarchy and hierarchy: An approach to study models of fermion masses and mixings
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Review of Particle Physics
text, January 2008

Planck 2015 results : X. Diffuse component separation: Foreground maps
journal, September 2016

Planck 2015 results : XVI. Isotropy and statistics of the CMB
journal, September 2016

Review of Particle Physics
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Planck 2015 results : XXVI. The Second
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Quark and Lepton Masses from Gaussian Landscapes
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Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes
text, January 2007

Neutrino mixing and mass hierarchy in Gaussian landscapes
text, January 2008

Planck 2013 results. XVI. Cosmological parameters
text, January 2013

Planck 2015 results. XIII. Cosmological parameters
text, January 2015

Anarchy and Neutrino Physics
text, January 2017

Strong Bayesian Evidence for the Normal Neutrino Hierarchy
text, January 2017

Statistical Test of Anarchy
text, January 2003

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    Works referencing / citing this record:

    Neutrino masses and their ordering: global data, priors and models
    journal, March 2018

    • Gariazzo, S.; Archidiacono, M.; de Salas, P. F.
    • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 03
    • DOI: 10.1088/1475-7516/2018/03/011

    Objective Bayesian analysis of neutrino masses and hierarchy
    journal, April 2018

    Bias due to neutrinos must not uncorrect'd go
    journal, September 2018

    • Vagnozzi, Sunny; Brinckmann, Thejs; Archidiacono, Maria
    • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 09
    • DOI: 10.1088/1475-7516/2018/09/001

    Tale of stable interacting dark energy, observational signatures, and the H 0 tension
    journal, September 2018

    • Yang, Weiqiang; Pan, Supriya; Valentino, Eleonora Di
    • Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 09
    • DOI: 10.1088/1475-7516/2018/09/019

    Status of Neutrino Properties and Future Prospects—Cosmological and Astrophysical Constraints
    journal, February 2018

    Neutrino Mass Ordering from Oscillations and Beyond: 2018 Status and Future Prospects
    journal, October 2018

    • de Salas, Pablo F.; Gariazzo, Stefano; Mena, Olga
    • Frontiers in Astronomy and Space Sciences, Vol. 5
    • DOI: 10.3389/fspas.2018.00036

    Maximum-Entropy Priors with Derived Parameters in a Specified Distribution
    journal, March 2019

    Maximum-Entropy Priors with Derived Parameters in a Specified Distribution.
    text, January 2019

    • Handley, Will; Millea, Marius
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.37947

    Neutrino masses and their ordering: Global Data, Priors and Models
    text, January 2018

    Objective Bayesian analysis of neutrino masses and hierarchy
    text, January 2018

    Phenomenology of Modified Gravity at Recombination
    text, January 2018

    Upper Bound of Neutrino Masses from Combined Cosmological Observations and Particle Physics Experiments
    text, January 2018

    Swampland Conjectures and Late-Time Cosmology
    text, January 2018

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      Figures / Tables found in this record:

      FIG. 1 (p. 2)figure
      FIG. 2 (p. 11)figure
      FIG. 3 (p. 12)figure
      FIG. 4 (p. 12)figure
      FIG. 5 (p. 13)figure
      Table I (p. 13)table
      FIG. 6 (p. 14)figure
      FIG. 7 (p. 15)figure
      Table II (p. 15)table
      FIG. 8 (p. 17)figure
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