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Title: Neutrino mass priors for cosmology from random matrices

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Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
FG02-13ER41958; SC0009924
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 97; Journal Issue: 4; Related Information: CHORUS Timestamp: 2018-02-13 14:19:17; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

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. 2018. "Neutrino mass priors for cosmology from random matrices". United States. doi:10.1103/PhysRevD.97.043510.
title = {Neutrino mass priors for cosmology from random matrices},
author = {Long, Andrew J. and Raveri, Marco and Hu, Wayne and Dodelson, Scott},
abstractNote = {},
doi = {10.1103/PhysRevD.97.043510},
journal = {Physical Review D},
number = 4,
volume = 97,
place = {United States},
year = 2018,
month = 2

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on February 13, 2019
Publisher's Accepted Manuscript

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  • Cosmological measurements of structure are placing increasingly strong constraints on the sum of the neutrino masses,more » $$\Sigma m_\nu$$, through Bayesian inference. Because these constraints depend on the choice for the prior probability $$\pi(\Sigma m_\nu)$$, 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 $$M_\nu$$, since this is the parameter appearing in the Lagrangian of the particle physics theory. Thus by specifying a probability distribution over $$M_\nu$$, and by including the known squared mass splittings, we predict a theoretical probability distribution over $$\Sigma m_\nu$$ that we interpret as a Bayesian prior probability $$\pi(\Sigma m_\nu)$$. We find that $$\pi(\Sigma m_\nu)$$ peaks close to the smallest $$\Sigma m_\nu$$ allowed by the measured mass splittings, roughly $$0.06 \, {\rm eV}$$ ($$0.1 \, {\rm eV}$$) 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 $$\pi(\Sigma m_\nu)$$ 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 $$\pi(\Sigma m_\nu)$$, 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
  • We use measurements of luminosity-dependent galaxy bias at several different redshifts, SDSS at z = 0.05, DEEP2 at z = 1 and LBGs at z = 3.8, combined with WMAP five-year cosmic microwave background anisotropy data and SDSS Red Luminous Galaxy survey three-dimensional clustering power spectrum to put constraints on cosmological parameters. Fitting this combined dataset, we show that the luminosity-dependent bias data that probe the relation between halo bias and halo mass and its redshift evolution are very sensitive to sum of the neutrino masses: in particular we obtain the upper limit of {Sigma}m{sub {nu}<}0.28 eV at the 95%more » confidence level for a {Lambda}CDM+m{sub {nu}}model, with a {sigma}8 equal to {sigma}8 = 0.759{+-}0.025 (1{sigma}). When we allow the dark energy equation of state parameter w to vary we find w -1.30{+-}0.19 for a general wCDM+m{sub {nu}}model with the 95% confidence level upper limit on the neutrino masses at {Sigma}m{sub {nu}<}0.59 eV. The constraint on the dark energy equation of state further improves to w = -1.125{+-}0.092 when using also ACBAR and supernovae Union data, in addition to above, with a prior on the Hubble constant from the Hubble Space Telescope. Finally, we have investigated the ability of future cosmic shear measurements, like those achievable with the proposed Euclid mission, to constrain differences in the mass of individual neutrino species.« less
  • Non-zero neutrino mass would affect the evolution of the Universe in observable ways, and a strong constraint on the mass can be achieved using combinations of cosmological data sets. We focus on the power spectrum of cosmic microwave background (CMB) anisotropies, the Hubble constant H{sub 0}, and the length scale for baryon acoustic oscillations (BAO) to investigate the constraint on the neutrino mass, m{sub ν}. We analyze data from multiple existing CMB studies (WMAP5, ACBAR, CBI, BOOMERANG, and QUAD), recent measurement of H{sub 0} (SHOES), with about two times lower uncertainty (5 %) than previous estimates, and recent treatments ofmore » BAO from the Sloan Digital Sky Survey (SDSS). We obtained an upper limit of m{sub ν} < 0.2eV (95 % C.L.), for a flat ΛCDM model. This is a 40 % reduction in the limit derived from previous H{sub 0} estimates and one-third lower than can be achieved with extant CMB and BAO data. We also analyze the impact of smaller uncertainty on measurements of H{sub 0} as may be anticipated in the near term, in combination with CMB data from the Planck mission, and BAO data from the SDSS/BOSS program. We demonstrate the possibility of a 5σ detection for a fiducial neutrino mass of 0.1 eV or a 95 % upper limit of 0.04 eV for a fiducial of m{sub ν} = 0 eV. These constraints are about 50 % better than those achieved without external constraint. We further investigate the impact on modeling where the dark-energy equation of state is constant but not necessarily -1, or where a non-flat universe is allowed. In these cases, the next-generation accuracies of Planck, BOSS, and 1 % measurement of H{sub 0} would all be required to obtain the limit m{sub ν} < 0.05−0.06 eV (95 % C.L.) for the fiducial of m{sub ν} = 0 eV. The independence of systematics argues for pursuit of both BAO and H{sub 0} measurements.« less
  • We extend our study of neutrino masses and mixings to the case of a 17-keV Dirac {tau} neutrino, which has reappeared in recent {beta}-decay experiments. A special set of Dirac submatrices is inputted which works well for quarks and yields a top-quark mass near 135 GeV. Unlike our previous Majorana neutrino study, however, we cannot simultaneously explain all the data including the 17-keV neutrino, its small {vert bar}{ital V}{sub {nu}{tau}}{ital e}{vert bar}{sup 2}=0.0085 coupling to the electron, the present accelerator neutrino oscillation bounds, and the preferred solar-neutrino nonadiabatic Mikheyev-Smirnov-Wolfenstein effect interpretation.
  • A new procedure proposed recently enables one to start from the quark and lepton mass and mixing data at the low scale and construct mass matrices which exhibit a simple SO(10) structure at the supersymmetric-grand-unification scale. We elaborate here on the numerical details which lead us to an SO(10) model for the quark and lepton mass matrices that explains the known quark data at the low scale along with the observed depletions of solar and atmospheric neutrinos. We also apply the procedure to a second scenario incorporating the solar-neutrino depletion and a 7 eV {tau} neutrino for the cocktail modelmore » of mixed dark matter but find the SO(10) model deduced in this case does not exhibit as simple a structure as that observed for the first scenario.« less