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Title: Neutrino mass priors for cosmology from random matrices

Journal Article · · Physical Review. D.
 [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)

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.

Research Organization:
Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States); Carnegie Mellon Univ., Pittsburgh, PA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); Kavli Foundation; National Aeronautics and Space Administration (NASA); National Science Foundation (NSF)
Grant/Contract Number:
SC0010118; AC02-07CH11359; PHY-1125897; FG02-13ER41958; NNX15AK22G; SC0009924
OSTI ID:
1413677
Alternate ID(s):
OSTI ID: 1420363; OSTI ID: 1594047; OSTI ID: 1755503
Report Number(s):
FERMILAB-PUB-17-572-A; arXiv:1711.08434; PRVDAQ; 1637562
Journal Information:
Physical Review. D., Vol. 97, Issue 4; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 30 works
Citation information provided by
Web of Science

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Cited By (17)

Neutrino masses and their ordering: global data, priors and models journal March 2018
Objective Bayesian analysis of neutrino masses and hierarchy journal April 2018
Bias due to neutrinos must not uncorrect'd go journal September 2018
Tale of stable interacting dark energy, observational signatures, and the H 0 tension journal September 2018
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
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
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
Bias due to neutrinos must not uncorrect'd go journal September 2018
Maximum-Entropy Priors with Derived Parameters in a Specified Distribution journal March 2019
Cosmological searches for the neutrino mass scale and mass ordering preprint January 2019
The Once and Present Standard Model of Elementary Particle Physics preprint January 2019

Figures / Tables (10)