pith. sign in

arxiv: 1907.08010 · v1 · pith:GMCWFNS4new · submitted 2019-07-18 · 🌌 astro-ph.CO · gr-qc· hep-ph

Cosmological searches for the neutrino mass scale and mass ordering

Sunny Vagnozzi This is my paper

Pith reviewed 2026-05-24 19:40 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords neutrino mass sumneutrino mass orderinglarge-scale structuregalaxy biascosmological constraintsdark energyCMB lensing
0
0 comments X

The pith

Cosmological data from large-scale structure yields an upper limit of 0.12 eV on the sum of neutrino masses and a weak preference for normal ordering driven by volume effects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The thesis reviews how large-scale structure observations encode information on the total mass of the three neutrino species. It presents an analysis that produces the tightest current cosmological upper bound of 0.12 eV and notes that the data mildly favor the normal mass ordering solely because more parameter space is available for that case. The work identifies that the conventional definition of galaxy bias produces an artificial scale dependence once neutrinos are massive, and it proposes a calibration method using CMB lensing-galaxy cross-correlations together with a corrected bias recipe. It further shows that neutrino-mass limits tighten in certain dynamical dark energy scenarios, which in turn amplifies the volume-driven preference for normal ordering.

Core claim

Large-scale structure data constrain the sum of neutrino masses to less than 0.12 eV. The same data display a weak preference for the normal mass ordering that originates in the larger available parameter volume rather than in any direct observational signature. The standard galaxy-bias definition becomes scale-dependent on large scales when neutrinos carry mass, an effect that must be removed by a new recipe if future surveys are to extract reliable neutrino information. In non-phantom dynamical dark energy models the neutrino-mass upper bound tightens relative to the Lambda-CDM case, strengthening the volume-driven ordering preference. Constraints on inflationary parameters remain stable,

What carries the argument

Scale-dependent galaxy bias in the presence of massive neutrinos, calibrated through CMB lensing-galaxy cross-correlations and corrected by a new bias recipe that removes spurious large-scale dependence.

If this is right

  • Non-phantom dynamical dark energy models produce a tighter upper limit on the neutrino mass sum than Lambda-CDM and therefore a stronger volume-driven preference for normal ordering.
  • If the corrected bias recipe is not used, future large-scale structure surveys will suffer systematic errors in neutrino-mass constraints.
  • Inflationary parameter determinations stay unchanged when assumptions about the neutrino sector are varied.
  • The volume effect that generates the mild ordering preference can be quantified with a simple statistical measure proposed in the analysis.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Adopting the new bias definition across analyses would reduce tension between cosmological and laboratory neutrino-mass bounds.
  • The volume-driven nature of the ordering preference implies that oscillation experiments, rather than cosmology alone, will ultimately decide the mass hierarchy.
  • Correlations between neutrino mass and dark energy parameters could serve as a consistency test once laboratory ordering results become available.

Load-bearing premise

The conventional definition of galaxy bias fails to remain scale-independent once neutrinos have non-zero mass.

What would settle it

A laboratory determination that the neutrino mass ordering is inverted would exclude or strongly disfavor the non-phantom dynamical dark energy models examined in the thesis.

Figures

Figures reproduced from arXiv: 1907.08010 by Sunny Vagnozzi.

Figure 2.1
Figure 2.1. Figure 2.1: Pie chart representing the energy budget of the Universe today, as we believe we understand it: less than 5% is in the form of matter we are familiar with, dubbed baryonic matter. Credits: The Conversation [187]. It is common practice to normalize the scale factor to take the value 1 today: a0 = 1 (the subscript 0 usually refers to quantities evaluated today). The time evolution of the scale factor can b… view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Evolution of energy density and density parameters of the various com￾ponents of the Universe. Upper panel: evolution of the energy densities ρi , in GeV4 , of photons (red solid curve), baryons (blue dashed curve), dark matter (green dashed curve), the cosmological constant (black solid curve), and massive neutrinos (with Mν = 0.06 eV, purple dashed curve) as a function of scale factor a. The three ver￾… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Evolution of the effective number of relativistic degrees of freedom g? (solid line) and the effective number of entropy degrees of freedom g s ? (dashed line) assuming the particle content of the Standard Model, as a function of the temperature of the Universe. It is clear that both g? and g s ? decrease when particles annihilate or become non-relativistic. However, two events during which g? and g s ? … view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: A visual representation of the two possible neutrino mass order￾ings/hierarchies. On the left side, the normal ordering, where m1 < m2 < m3, and the atmospheric mass-squared splitting is positive. On the right side, the inverted or￾dering, where m3 < m1 < m2 and the atmospheric mass-squared splitting is negative. The relative proportion of red (νe), blue (νµ), and green (ντ ) in the box correspond￾ing to… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Sum of the neutrino masses Mν as a function of the mass of the lightest eigenstate mlight for NO (blue line) and IO (green line). The nearly indistinguishable width of the two lines is representative of the current 3σ uncertainties on the two mass￾squared splittings. The horizontal red dashed line represents the current cosmological upper limit on the sum of the neutrino masses Mν < 0.12 eV obtained in P… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: A schematic representation of how Thomson scattering of radiation with quadrupole anisotropy generates linear polarization. Reproduced from [847] with per￾mission from Elsevier. primordial gravitational waves from inflation. Polarization of the CMB is an incredibly com￾plex topic, especially from the mathematical point of view. My goal here will be to provide the reader a heuristic level of understanding… view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Temperature power spectrum from the Planck 2015 data release. Upper panel: the blue points are the actual measurements with error bars (nearly invisible for ` 30), whereas the red curve is the theoretical power spectrum computed using the best-fit parameters obtained analysing temperature and large-scale polarization data. Notice that, as per standard convention in the field, the quantity plotted on the … view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Impact of varying the six fundamental ΛCDM parameters on the CMB temperature power spectrum. The chosen baseline model has ωb = 0.02, ωc = 0.12, 100θs = 1.054, τ = 0.072, As = 2.16 × 10−9 , and ns = 0.96. Derived parameters of particular interest are h = 0.7, ΩΛ = 0.713, zeq = 3345.55, and 100θd = 0.167. The spectra have been produced through the Boltzmann solver CAMB [498], which takes h as input and no… view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Impact of varying the six fundamental ΛCDM parameters on the matter power spectrum. The chosen baseline model has ωb = 0.02, ωc = 0.12, As = 2.16×10−9 , and ns = 0.96. Derived parameters of particular interest are h = 0.7, ΩΛ = 0.713, zeq = 3345.55, and 100θd = 0.167. The spectra have been produced through the Boltzmann solver CAMB [498]. When ωb and ωc, and ωb/ωc are varied, I manually adjust h to keep … view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Two point-correlation function measured from the CMASS sample of the BOSS DR10 galaxies. The “bump” at comoving separations of ' 150 Mpc is clearly visible. Credits: BOSS collaboration [950]. and dV2, separated by a distance r. Then, the expected number of pairs of galaxies with one galaxy in dV1 and the other galaxy in dV2, hnpairi, is given by: hnpairi = ¯n 2 [1 + ξ(r)] dV1dV2 . (4.30) Therefore, ξ(r) … view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Cartoon version of BAOs, showing spheres of baryons around initial dark matter clumps, with an excess clustering at a scale corresponding to the sound horizon at decoupling. Credits: BOSS collaboration [950]. in question, and indirectly measure the low-redshift expansion rate of the Universe. If one has sufficient sensitivity as to separate line-of-sight and transverse separations, the two can be used to… view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Impact of increasing the sum of the neutrino masses Mν on the CMB temperature power spectrum. Upper panel: the black curve is the power spectrum for the baseline model where Mν = 0.06 eV. In addition, we set h = 0.7, ωc = 0.12, and ΩΛ = 0.713. The other three curves are obtained for Mν = 1.8 eV, where the increase in Mν is compensated by setting h = 74.48 (blue curve), ωc = 0.10144 (red curve), and ΩΛ = … view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Impact of increasing the sum of the neutrino masses Mν on the CMB temperature power spectrum, adjusting h and ΩΛ to keep θs and zeq fixed at the expense of a small shift in zΛ. Upper panel: the black curve is the power spectrum for the baseline model where Mν = 0.06 eV, h = 0.7, and ΩΛ = 0.713. The green (red) curve is obtained for Mν = 1.8 eV (Mν = 0.9 eV), where the increase in Mν is compensated for b… view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Impact of increasing the effective number of neutrinos Neff on the CMB temperature power spectrum. Upper panel: the black curve is the power spectrum for the baseline model where Neff = 0. In addition, we set ωc = 0.12 and h = 0.7. The dashed blue curve is obtained for Neff = 3.046, keeping ωc and h fixed. The other three curves are obtained for Neff = 3.046 (solid blue curve), Neff = 2 (solid green cur… view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Impact of increasing the effective number of neutrinos Neff on the CMB temperature power spectrum while adjusting the Helium fraction Yp to keep the damp￾ing scale rd fixed. Upper panel: the black curve is the power spectrum for a baseline model where Neff = 3.046. In addition, we set ωc = 0.12, h = 0.7, and Yp = 0.24. The blue curve is obtained by increasing Neff = 4 and compensating this increase by s… view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: Impact of increasing the sum of the neutrino masses Mν on the linear matter power spectrum, keeping ωb and ωc (and hence zeq) fixed, and increasing h to keep Ωm fixed. Upper panel: the black curve is the power spectrum for the baseline model where Mν = 0.06 eV, ωb = 0.02, ωc = 0.12, h = 0.7, and hence Ωm = 0.287. The blue (red) [green] curves are obtained for Mν = 1.8 eV (Mν = 0.9 eV) [Mν = 0.6 eV], whe… view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: Impact of increasing the effective number of neutrinos Neff on the linear matter power spectrum, keeping ωb and ωc (and hence zeq) fixed, and increasing h to keep Ωm fixed. Upper panel: the black curve is the power spectrum for the baseline model where Mν = 0.06 eV, ωb = 0.02, ωc = 0.12, h = 0.7, and hence Ωm = 0.287. The blue (red) [green] curves are obtained for Mν = 1.8 eV (Mν = 0.9 eV) [Mν = 0.6 eV]… view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Top panel: nonlinear galaxy power spectrum computed using CAMB+Halofit (red curve), compared with the same quantity computed using the Coy￾ote emulator. Both quantities are plotted assuming the Planck 2015 best-fit parameters and Mν = 0 eV and a bias b ≈ 2. The green triangles denote the galaxy power spec￾trum measured from the BOSS DR12 CMASS sample, whereas the purple circles denote the galaxy power sp… view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Posteriors on Mν (normalized to their maximum values) obtained using different dataset combinations. The figure should be read as follows: to make the BAO vs P(k) comparison, choose a given color and compare the solid curve [P(k)] against the dashed curve [BAO]. It is clear that BAO (dashed curves) leads to tighter constraints. Notice that the black curves are obtained including a prior on H0 based on th… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Measured CMB lensing convergence-galaxy overdensity cross-power spectrum from cross-correlating Planck 2015 lensing maps with galaxies from the BOSS DR11 CMASS sample (blue points), compared against the theory predic￾tions (green curve). Theory predictions are made assuming a scale-dependent bias bcross(k) with parameters a and c fixed to their central values inferred from the PlanckTT+lowP+C κg ` +P(k) … view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Posterior distributions for Mν (normalized to their maximum values) ob￾tained using different datasets and making different assumptions on the galaxy bias: CMB (PlanckTT+lowP; black curve), CMB+P(k) (BOSS DR12 CMASS) with con￾stant bias (from Paper I [1012]; red curve), CMB+C κg ` (BOSS DR11 CMASS × Planck 2015 lensing) using scale-dependent bcross(k) (from Eq. (6.8); green curve), CMB+P(k) using scale-d… view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: The impact of not correctly accounting for the NISDB effect when ana￾lyzing mock galaxy clustering data from Euclid. Left panel: one-dimensional posterior distributions for Mν normalized to their maximum values, when the NISDB effect is correctly accounted for (blue solid), or not accounted for (red dashed). The dot-dashed vertical line denotes the input fiducial value Mν = 0.06 eV. Right panel: triangul… view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Left panel: one-dimensional posterior distributions for Mν normalized to their maximum values, assuming ΛCDM (black), the w0waCDM model (blue), and the NPDDE model (red), and using the base (solid) or pol (dashed) dataset. The dot-dashed vertical line denotes Mν = 0.1 eV, the minimum value of the sum of the neutrino masses allowed for the inverted ordering. Right panel: one-dimensional posterior distribu… view at source ↗
Figure 6.7
Figure 6.7. Figure 6.7: Marginalized 68% and 95% confidence intervals for ns for different choices of cosmological models (ΛCDM, ΛCDM+r, ΛCDM+Mν, and ΛCDM+r+Mν), cosmo￾logical datasets (combinations of PlanckTT+lowP, BAO, and BK14 ), and approxima￾tions on the neutrino mass spectrum (NO or 1mass/3deg approximations). The solid bold lines are obtained using the exact NO modelling, solid light lines using the exact IO modelling, … view at source ↗
Figure 6.8
Figure 6.8. Figure 6.8: Marginalized 68% and 95% confidence intervals for ns for different choices of cosmological models (ΛCDM+Neff, ΛCDM+r+Neff, ΛCDM+Neff+Mν, and ΛCDM+r+Neff+Mν), cosmological datasets (combinations of PlanckTT+lowP, BAO, and BK14 ), and assumptions about the neutrino effective number (“broad” 0 ≤ Neff ≤ 10 prior or “hard” Neff ≤ 3.046 prior). Solid lines are for the “broad” prior while dashed lines are for t… view at source ↗
Figure 6.9
Figure 6.9. Figure 6.9: 68% and 95% C.L. joint probability contours in the ns-r plane for the datasets and models indicated. The predictions for the cosine natural inflation model are shown in purple for 46 ≤ N∗ ≤ 60, with N∗ is the number of e-folds of inflation. Left panel: contours computed assuming NO. Right panel: “h” and “b” stand for the hard (Neff ≤ 3.046) and broad (0 ≤ Neff ≤ 10) priors imposed on Neff, contours compu… view at source ↗
read the original abstract

In this thesis, I describe a number of recent important developments in neutrino cosmology on three fronts. Firstly, focusing on Large-Scale Structure (LSS) data, I will show that current cosmological probes contain a wealth of information on the sum of the neutrino masses. I report on the analysis leading to the currently best upper limit on the sum of the neutrino masses of $0.12\,{\rm eV}$. I show how cosmological data exhibits a weak preference for the normal neutrino mass ordering because of parameter space volume effects, and propose a simple method to quantify this preference. Secondly, I will discuss how galaxy bias represents a severe limitation towards fully capitalizing on the neutrino information hidden in LSS data. I propose a method for calibrating the scale-dependent galaxy bias using CMB lensing-galaxy cross-correlations. Moreover, in the presence of massive neutrinos, the usual definition of bias becomes inadequate, as it leads to a scale-dependence on large scales which has never been accounted for. I show that failure to define the bias appropriately will be a problem for future LSS surveys, and propose a simple recipe to account for the effect of massive neutrinos on galaxy bias. Finally, I discuss implications of correlations between neutrino parameters and other cosmological parameters. In non-phantom dynamical dark energy models, the upper limit on the sum of the neutrino masses becomes tighter than the $\Lambda$CDM limit. Therefore, such models exhibit an even stronger preference for the normal ordering, and their viability could be jeopardized should near-future laboratory experiments determine that the mass ordering is inverted. I then discuss correlations between neutrino and inflationary parameters. I find that our determination of inflationary parameters is stable against assumptions about the neutrino sector. (abridged)

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. This thesis summarizes developments in neutrino cosmology from LSS and CMB data. It reports that current probes yield a best upper limit of 0.12 eV on the sum of neutrino masses, with cosmological data showing a weak preference for normal mass ordering driven by parameter-space volume effects. It identifies galaxy bias as a key limitation, noting that the standard bias definition produces unaccounted scale dependence on large scales when neutrinos are massive, and proposes calibration via CMB lensing-galaxy cross-correlations plus a recipe to correct for neutrino effects on bias. Additional sections examine how non-phantom dynamical dark energy tightens the mass-sum limit (strengthening the normal-ordering preference) and how neutrino assumptions leave inflationary parameters stable.

Significance. If the central results hold, the work demonstrates the constraining power of existing LSS+CMB datasets on neutrino masses and supplies a concrete methodological explanation (volume effects) for the observed ordering preference. The identification of a previously unaccounted scale-dependent bias effect, together with proposed calibration and correction recipes, directly addresses a systematic that will become load-bearing for next-generation surveys. The parameter-correlation analyses provide useful context on degeneracies with dark energy and inflation.

major comments (2)
  1. [Abstract / introduction (limit and ordering preference)] The 0.12 eV upper limit is presented as the best current constraint derived from LSS analyses, yet the manuscript later states that the usual galaxy-bias definition produces an unaccounted scale dependence on large scales in the presence of massive neutrinos. It is therefore necessary to clarify whether the analyses underlying the quoted limit employed the standard bias definition or the proposed correction; if the former, the posterior on Σmν (and the volume-effect ordering preference) could shift. This directly affects the load-bearing claim in the abstract and introduction.
  2. [Section on galaxy bias and neutrino effects] The statement that the usual bias definition 'leads to a scale-dependence on large scales which has never been accounted for' and 'will be a problem for future LSS surveys' is presented without a quantitative estimate of the induced bias on Σmν or on the ordering preference. A concrete forecast or re-analysis showing the magnitude of the shift would be required to substantiate that the effect is severe enough to warrant the proposed recipe.
minor comments (2)
  1. [Abstract] The abstract refers to 'the analysis leading to' the 0.12 eV limit but supplies no dataset list, likelihood details, or reference to the specific publication; adding these would improve traceability.
  2. [Throughout] Notation for the neutrino mass sum (Σmν vs. mν) and for the ordering preference metric should be defined at first use and used consistently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful comments on our thesis. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: [Abstract / introduction (limit and ordering preference)] The 0.12 eV upper limit is presented as the best current constraint derived from LSS analyses, yet the manuscript later states that the usual galaxy-bias definition produces an unaccounted scale dependence on large scales in the presence of massive neutrinos. It is therefore necessary to clarify whether the analyses underlying the quoted limit employed the standard bias definition or the proposed correction; if the former, the posterior on Σmν (and the volume-effect ordering preference) could shift. This directly affects the load-bearing claim in the abstract and introduction.

    Authors: The 0.12 eV upper limit is derived from previously published LSS analyses that used the standard definition of galaxy bias. The thesis summarizes these results and separately identifies the scale-dependent bias issue as a limitation for future analyses, proposing a correction recipe. We will revise the manuscript to explicitly state that the quoted limit comes from standard-bias analyses and that the proposed correction is intended for improved future constraints. This clarification will address the potential for shifts in the posterior. revision: yes

  2. Referee: [Section on galaxy bias and neutrino effects] The statement that the usual bias definition 'leads to a scale-dependence on large scales which has never been accounted for' and 'will be a problem for future LSS surveys' is presented without a quantitative estimate of the induced bias on Σmν or on the ordering preference. A concrete forecast or re-analysis showing the magnitude of the shift would be required to substantiate that the effect is severe enough to warrant the proposed recipe.

    Authors: We acknowledge that a quantitative forecast would provide stronger substantiation. However, the primary contribution of this section is the identification of the unaccounted scale dependence and the proposal of a calibration method using CMB lensing cross-correlations along with a correction recipe. The severity is argued qualitatively based on the fact that the effect appears on large scales where neutrino mass effects are most prominent. A full quantitative assessment would require dedicated simulations or re-analyses not included in the current thesis scope, but we can add a brief discussion noting the expected impact for next-generation surveys. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected; results drawn from external data analyses

full rationale

The reported 0.12 eV upper limit and ordering preference are presented as outcomes of existing LSS+CMB data analyses rather than internal derivations that loop back to fitted parameters or self-citations. The volume-effect explanation for the ordering preference is explicitly identified as a modeling feature, not a self-referential prediction. Proposed bias corrections are forward-looking recipes and do not redefine or force the prior limits. No load-bearing step reduces by construction to the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are detailed beyond standard cosmological model assumptions used in parameter estimation from LSS and CMB data.

pith-pipeline@v0.9.0 · 5842 in / 1091 out tokens · 39792 ms · 2026-05-24T19:40:34.814250+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity

    astro-ph.CO 2026-01 unverdicted novelty 5.0

    The w†VCDM model shows a statistically significant preference for late-time quintessence-phantom crossing dark energy, raises the Hubble constant, and satisfies neutrino mass and Neff constraints from current cosmolog...

Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · cited by 1 Pith paper · 218 internal anchors

  1. [1]

    Tanabashi et al.,Review of Particle Physics, Phys

    Particle Data Group collaboration, M. Tanabashi et al.,Review of Particle Physics, Phys. Rev. D98 (2018) 030001

    work page 2018

  2. [2]

    M. C. González-García, M. Maltoni, J. Salvadó and T. Schwetz,Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123, [1209.3023]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  3. [3]

    M. C. González-García, M. Maltoni and T. Schwetz,Updated fit to three neutrino mixing: status of leptonic CP violation, JHEP 11 (2014) 052, [1409.5439]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  4. [4]

    M. C. González-García, M. Maltoni and T. Schwetz,Global Analyses of Neutrino Oscillation Experiments, Nucl. Phys. B908 (2016) 199–217, [1512.06856]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  5. [5]

    Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity

    I. Esteban, M. C. González-García, M. Maltoni, I. Martínez-Soler and T. Schwetz,Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP 01 (2017) 087, [1611.01514]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    P. F. de Salas, D. V. Forero, C. A. Ternes, M. Tórtola and J. W. F. Valle,Status of neutrino oscillations 2018: 3σ hint for normal mass ordering and improved CP sensitivity, Phys. Lett. B782 (2018) 633–640, [1708.01186]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    P. F. de Salas, S. Gariazzo, O. Mena, C. A. Ternes and M. Tórtola,Neutrino Mass Ordering from Oscillations and Beyond: 2018 Status and Future Prospects, Front. Astron. Space Sci.5 (2018) 36, [1806.11051]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  8. [8]

    Can cosmology detect hierarchical neutrino masses?

    S. Hannestad,Can cosmology detect hierarchical neutrino masses?, Phys. Rev. D67 (2003) 085017, [astro-ph/0211106]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  9. [9]

    Dark Energy and Neutrino Masses from Future Measurements of the Expansion History and Growth of Structure

    S. Joudaki and M. Kaplinghat,Dark Energy and Neutrino Masses from Future Measurements of the Expansion History and Growth of Structure, Phys. Rev. D86 (2012) 023526, [1106.0299]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  10. [10]

    Measuring the neutrino mass from future wide galaxy cluster catalogues

    C. Carbone, C. Fedeli, L. Moscardini and A. Cimatti,Measuring the neutrino mass from future wide galaxy cluster catalogues, JCAP 1203 (2012) 023, [1112.4810]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  11. [11]

    Measuring neutrino masses with a future galaxy survey

    J. Hamann, S. Hannestad and Y. Y. Y. Wong,Measuring neutrino masses with a future galaxy survey, JCAP 1211 (2012) 052, [1209.1043]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  12. [12]

    Towards a cosmological neutrino mass detection

    R. Allison, P. Caucal, E. Calabrese, J. Dunkley and T. Louis,Towards a cosmological neutrino mass detection, Phys. Rev. D92 (2015) 123535, [1509.07471]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  13. [13]

    Physical effects involved in the measurements of neutrino masses with future cosmological data

    M. Archidiacono, T. Brinckmann, J. Lesgourgues and V. Poulin,Physical effects involved in the measurements of neutrino masses with future cosmological data, JCAP 1702 (2017) 052, [1610.09852]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  14. [14]

    Boyle and E

    A. Boyle and E. Komatsu,Deconstructing the neutrino mass constraint from galaxy redshift surveys, JCAP 1803 (2018) 035, [1712.01857]

    work page arXiv 2018

  15. [15]

    Cosmology in the era of Euclid and the Square Kilometre Array

    T. Sprenger, M. Archidiacono, T. Brinckmann, S. Clesse and J. Lesgourgues,Cosmology in the era of Euclid and the Square Kilometre Array, JCAP 1902 (2019) 047, [1801.08331]

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  16. [16]

    Neutrino masses and beyond-$\Lambda$CDM cosmology with LSST and future CMB experiments

    S. Mishra-Sharma, D. Alonso and J. Dunkley,Neutrino masses and beyond-ΛCDM cosmology with LSST and future CMB experiments, Phys. Rev. D97 (2018) 123544, [1803.07561]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [17]

    The promising future of a robust cosmological neutrino mass measurement

    T. Brinckmann, D. C. Hooper, M. Archidiacono, J. Lesgourgues and T. Sprenger,The promising future of a robust cosmological neutrino mass measurement, JCAP 1901 (2019) 059, [1808.05955]

    work page internal anchor Pith review Pith/arXiv arXiv 1901

  18. [18]

    C. D. Kreisch, A. Pisani, C. Carbone, J. Liu, A. J. Hawken, E. Massara et al.,Massive Neutrinos Leave Fingerprints on Cosmic Voids, 1808.07464

    work page internal anchor Pith review Pith/arXiv arXiv

  19. [19]

    The Simons Observatory: Science goals and forecasts

    Simons Observatorycollaboration, P. Ade et al.,The Simons Observatory: Science goals and forecasts, JCAP 1902 (2019) 056, [1808.07445]. 106 References

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  20. [20]

    B. Yu, R. Z. Knight, B. D. Sherwin, S. Ferraro, L. Knox and M. Schmittfull,Towards Neutrino Mass from Cosmology without Optical Depth Information, 1809.02120

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    Boyle,Understanding the neutrino mass constraints achievable by combining CMB lensing and spectroscopic galaxy surveys, 1811.07636

    A. Boyle,Understanding the neutrino mass constraints achievable by combining CMB lensing and spectroscopic galaxy surveys, 1811.07636

    work page arXiv

  22. [22]

    PICO: Probe of Inflation and Cosmic Origins

    NASA PICO collaboration, S. Hanany et al.,PICO: Probe of Inflation and Cosmic Origins, 1902.10541

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  23. [23]

    Electroweak Symmetry Breaking and BSM Physics (A Review)

    G. Bhattacharyya,Electroweak Symmetry Breaking and BSM Physics (A Review), Pramana 72 (2009) 37–54, [0807.3883]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    J. D. Lykken,Beyond the Standard Model, inCERN Yellow Report CERN-2010-002, 101-109, 2010, 1005.1676

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  25. [25]

    B. C. Allanach,Beyond the Standard Model Lectures for the 2016 European School of High-Energy Physics, inProceedings, 2016 European School of High-Energy Physics (ESHEP2016): Skeikampen, Norway, June 15-28 2016, pp. 123–152, 2017,1609.02015

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  26. [26]

    Physics Beyond the Standard Model

    R. Rosenfeld,Physics Beyond the Standard Model, inProceedings, 8th CERN–Latin-American School of High-Energy Physics (CLASHEP2015): Ibarra, Ecuador, March 05-17, 2015, pp. 159–164, 2016,1708.00800

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  27. [27]

    Flavour anomalies: a review

    ATLAS, CMS, LHCb collaboration, E. Graverini,Flavour anomalies: a review, J. Phys. Conf. Ser. 1137 (2019) 012025, [1807.11373]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  28. [28]

    Beyond the Cosmological Standard Model

    A. Joyce, B. Jain, J. Khoury and M. Trodden,Beyond the Cosmological Standard Model, Phys. Rept. 568 (2015) 1–98, [1407.0059]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  29. [29]

    Beyond $\Lambda$CDM: Problems, solutions, and the road ahead

    P. Bull et al.,Beyond ΛCDM: Problems, solutions, and the road ahead, Phys. Dark Univ.12 (2016) 56–99, [1512.05356]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  30. [30]

    W. L. Freedman,Cosmology at a Crossroads, Nat. Astron.1 (2017) 0121, [1706.02739]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    Crack in the cosmological paradigm

    E. Di Valentino,Crack in the cosmological paradigm, Nat. Astron.1 (2017) 569–570, [1709.04046]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  32. [32]

    On the tension between Large Scale Structures and Cosmic Microwave Background

    M. Douspis, L. Salvati and N. Aghanim,On the Tension between Large Scale Structures and Cosmic Microwave Background, PoS EDSU2018 (2018) 037, [1901.05289]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [33]

    Mandl and G

    F. Mandl and G. Shaw,Quantum Field Theory. 1985

    work page 1985

  34. [34]

    T. P. Cheng and L. F. Li,Gauge Theory of Elementary particle physics. 1984

    work page 1984

  35. [35]

    G. L. Kane,Modern Elementary Particle Physics. Cambridge University Press, 2017

    work page 2017

  36. [36]

    I. J. R. Aitchison and A. J. G. Hey,Gauge Theories in Particle Physics: A Practical Introduction. 1989

    work page 1989

  37. [37]

    P. D. B. Collins, A. D. Martin and E. J. Squires,Particle Physics and Cosmology. 1989

    work page 1989

  38. [38]

    J. F. Donoghue, E. Golowich and B. R. Holstein,Dynamics of the standard model, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol.2 (1992) 1–540

    work page 1992

  39. [39]

    W. N. Cottingham and D. A. Greenwood,An introduction to the standard model of particle physics. Cambridge University Press, 2007

    work page 2007

  40. [40]

    Griffiths,Introduction to elementary particles

    D. Griffiths,Introduction to elementary particles. 2008

    work page 2008

  41. [41]

    Langacker,The standard model and beyond

    P. Langacker,The standard model and beyond. 2010

    work page 2010

  42. [42]

    M. D. Schwartz,Quantum Field Theory and the Standard Model. Cambridge University Press, 2014

    work page 2014

  43. [43]

    Evidence for oscillation of atmospheric neutrinos

    Super-Kamiokande collaboration, Y. Fukuda et al.,Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett.81 (1998) 1562–1567, [hep-ex/9807003]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  44. [44]

    Minkowski,µ→ eγ at a Rate of One Out of109 Muon Decays?, Phys

    P. Minkowski,µ→ eγ at a Rate of One Out of109 Muon Decays?, Phys. Lett.67B (1977) 421–428

    work page 1977

  45. [45]

    Yanagida,Horizontal gauge symmetry and masses of neutrinos, Conf

    T. Yanagida,Horizontal gauge symmetry and masses of neutrinos, Conf. Proc.C7902131 (1979) 95–99

    work page 1979

  46. [46]

    Complex Spinors and Unified Theories

    M. Gell-Mann, P. Ramond and R. Slansky,Complex Spinors and Unified Theories, Conf. Proc. C790927 (1979) 315–321, [1306.4669]

    work page internal anchor Pith review Pith/arXiv arXiv 1979

  47. [47]

    R. N. Mohapatra and G. Senjanović,Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett.44 (1980) 912

    work page 1980

  48. [48]

    Schechter and J

    J. Schechter and J. W. F. Valle,Neutrino Masses in SU(2) x U(1) Theories, Phys. Rev. D22 (1980) 2227. References 107

    work page 1980

  49. [49]

    Magg and C

    M. Magg and C. Wetterich,Neutrino Mass Problem and Gauge Hierarchy, Phys. Lett. 94B (1980) 61–64

    work page 1980

  50. [50]

    Lazarides, Q

    G. Lazarides, Q. Shafi and C. Wetterich,Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B181 (1981) 287–300

    work page 1981

  51. [51]

    R. N. Mohapatra and G. Senjanović,Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, Phys. Rev. D23 (1981) 165

    work page 1981

  52. [52]

    Wetterich,Neutrino Masses and the Scale of B-L Violation, Nucl

    C. Wetterich,Neutrino Masses and the Scale of B-L Violation, Nucl. Phys. B187 (1981) 343–375

    work page 1981

  53. [53]

    R. Foot, H. Lew, X. G. He and G. C. Joshi,Seesaw Neutrino Masses Induced by a Triplet of Leptons, Z. Phys. C44 (1989) 441

    work page 1989

  54. [54]

    Pathways to Naturally Small Neutrino Masses

    E. Ma,Pathways to naturally small neutrino masses, Phys. Rev. Lett.81 (1998) 1171–1174, [hep-ph/9805219]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  55. [55]

    Heavy Triplet Leptons and New Gauge Boson

    E. Ma and D. P. Roy,Heavy triplet leptons and new gauge boson, Nucl. Phys. B644 (2002) 290–302, [hep-ph/0206150]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  56. [56]

    Zee,Charged Scalar Field and Quantum Number Violations, Phys

    A. Zee,Charged Scalar Field and Quantum Number Violations, Phys. Lett. 161B (1985) 141–145

    work page 1985

  57. [57]

    Zee,Quantum Numbers of Majorana Neutrino Masses, Nucl

    A. Zee,Quantum Numbers of Majorana Neutrino Masses, Nucl. Phys. B264 (1986) 99–110

    work page 1986

  58. [58]

    K. S. Babu,Model of ’Calculable’ Majorana Neutrino Masses, Phys. Lett. B203 (1988) 132–136

    work page 1988

  59. [59]

    The $\nu$MSM, Dark Matter and Neutrino Masses

    T. Asaka, S. Blanchet and M. Shaposhnikov,The nuMSM, dark matter and neutrino masses, Phys. Lett. B631 (2005) 151–156, [hep-ph/0503065]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  60. [60]

    The $\nu$MSM, Dark Matter and Baryon Asymmetry of the Universe

    T. Asaka and M. Shaposhnikov,The nuMSM, dark matter and baryon asymmetry of the universe, Phys. Lett. B620 (2005) 17–26, [hep-ph/0505013]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  61. [61]

    The role of sterile neutrinos in cosmology and astrophysics

    A. Boyarsky, O. Ruchayskiy and M. Shaposhnikov,The Role of sterile neutrinos in cosmology and astrophysics, Ann. Rev. Nucl. Part. Sci.59 (2009) 191–214, [0901.0011]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  62. [62]

    S. M. Boucenna, S. Morisi and J. W. F. Valle,The low-scale approach to neutrino masses, Adv. High Energy Phys.2014 (2014) 831598, [1404.3751]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  63. [63]

    S. F. King,Models of Neutrino Mass, Mixing and CP Violation, J. Phys. G42 (2015) 123001, [1510.02091]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  64. [64]

    S. F. King,Neutrino mass models, Rept. Prog. Phys.67 (2004) 107–158, [hep-ph/0310204]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  65. [65]

    Y. Cai, J. Herrero-García, M. A. Schmidt, A. Vicente and R. R. Volkas,From the trees to the forest: a review of radiative neutrino mass models, Front.in Phys.5 (2017) 63, [1706.08524]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  66. [66]

    R. N. Mohapatra and A. Y. Smirnov,Neutrino Mass and New Physics, Ann. Rev. Nucl. Part. Sci. 56 (2006) 569–628, [hep-ph/0603118]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  67. [67]

    Discrete Flavor Symmetries and Models of Neutrino Mixing

    G. Altarelli and F. Feruglio,Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701–2729, [1002.0211]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  68. [68]

    GUT and flavor models for neutrino masses and mixing

    D. Meloni,GUT and flavor models for neutrino masses and mixing, Front.in Phys.5 (2017) 43, [1709.02662]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  69. [69]

    Current unknowns in the three neutrino framework

    F. Capozzi, E. Lisi, A. Marrone and A. Palazzo,Current unknowns in the three neutrino framework, Prog. Part. Nucl. Phys.102 (2018) 48–72, [1804.09678]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  70. [70]

    Hubble,A relation between distance and radial velocity among extra-galactic nebulae, Proc

    E. Hubble,A relation between distance and radial velocity among extra-galactic nebulae, Proc. Nat. Acad. Sci.15 (1929) 168–173

    work page 1929

  71. [71]

    Lemaître,A Homogeneous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae, Annales Soc

    G. Lemaître,A Homogeneous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae, Annales Soc. Sci. Bruxelles A47 (1927) 49–59

    work page 1927

  72. [72]

    Zwicky,Die Rotverschiebung von extragalaktischen Nebeln, Helv

    F. Zwicky,Die Rotverschiebung von extragalaktischen Nebeln, Helv. Phys. Acta6 (1933) 110–127

    work page 1933

  73. [73]

    R. A. Alpher, H. Bethe and G. Gamow,The origin of chemical elements, Phys. Rev. 73 (1948) 803–804

    work page 1948

  74. [74]

    R. A. Alpher and R. C. Herman,On the Relative Abundance of the Elements, Phys. Rev. 74 (1948) 1737–1742

    work page 1948

  75. [75]

    A. A. Penzias and R. W. Wilson,A Measurement of excess antenna temperature at 4080-Mc/s, Astrophys. J.142 (1965) 419–421

    work page 1965

  76. [76]

    R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson,Cosmic Black-Body Radiation, Astrophys. J.142 (1965) 414–419

    work page 1965

  77. [77]

    D. J. Fixsen, E. S. Cheng, J. M. Gales, J. C. Mather, R. A. Shafer and E. L. Wright,The Cosmic Microwave Background spectrum from the full COBE FIRAS data set, Astrophys. J.473 (1996) 576, [astro-ph/9605054]. 108 References

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  78. [78]

    COBE collaboration, G. F. Smoot et al.,Structure in the COBE differential microwave radiometer first year maps, Astrophys. J.396 (1992) L1–L5

    work page 1992

  79. [79]

    WMAP collaboration, C. L. Bennett et al.,The Microwave Anisotropy Probe (MAP) mission, Astrophys. J.583 (2003) 1–23, [astro-ph/0301158]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  80. [80]

    WMAP collaboration, D. N. Spergel et al.,Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology, Astrophys. J. Suppl.170 (2007) 377, [astro-ph/0603449]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

Showing first 80 references.