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REVIEW 5 major objections 5 minor 111 references

Missing matter in galaxies as a neutrino mixing effect

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that the vacuum state associated with neutrino flavor mixing behaves like cold dark matter in curved spacetime and adds a Yukawa correction to the Newtonian potential, potentially explaining flat galaxy rotation curves…

desk verdict Clean dust-EOS proof for the flavor vacuum, but the Yukawa claim rests on an unproved mode ansatz. read the letter →

arxiv 2411.17319 v1 pith:MU4GE3YK submitted 2024-11-26 hep-ph astro-ph.GAgr-qchep-th

Antonio Capolupo , Salvatore Capozziello , Gabriele Pisacane , Aniello Quaranta This is my paper · ORCID
classification hep-phastro-ph.GAgr-qchep-th PACS 04.62.+v95.35.+d14.60.Pq98.62.Gq
keywords neutrinomixingflavorvacuumdarkmattercoldequationofstateYukawacorrectionflatrotationcurvesbaryonicmass-rotationvelocityrelationquantumfieldtheoryincurvedspacetime
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that the vacuum associated with neutrino flavor mixing—the flavor vacuum—behaves, in curved spacetime, like a pressureless fluid with the equation of state of cold dark matter, and that at galactic scales it adds a Yukawa correction to the Newtonian potential. If correct, the flat rotation curves of spiral galaxies could be a gravitational imprint of ordinary neutrino mixing, potentially tracing part of the dark-matter phenomenon to already-known physics. The authors derive this from the vacuum expectation value of the stress-energy tensor in a weak-field, spherically symmetric spacetime, then show that the resulting potential reproduces the baryonic mass–rotation velocity relation for spiral and gas-rich galaxy samples.

What carries the argument

The central object is the flavor vacuum $|0_F(\tau)\rangle$, the non-trivial vacuum state produced by the time-dependent mixing generator that rotates mass fields into flavor fields. It has a condensate structure of particle–antiparticle pairs, and its energy-momentum content is computed through the vacuum expectation value of the normal-ordered stress tensor. The key algebraic step is that every spatial bilinear of the two neutrino fields is invariant under the mixing generator, so all spatial components of the stress tensor vanish and only $T_{00}$ survives. The weak-field derivation then relies on replacing the flat-space radial modes with $(1+\tfrac{3}{2}V(R))$ times those modes, which preserves the mode normalization to first order in $V(R)$ and converts the flat-space energy density $4\sin^2\Theta\,K$ into $4\sin^2\Theta\,K(1+4V(R))$. Solving the Poisson equation with this source gives the Yukawa correction.

What would settle it

Solve the exact radial neutrino mode equations (Eq. 23) for a weak-field metric and check whether the rescaled flat-space modes satisfy them to first order in $V(R)$; if the residual is not first-order small, the formula $T_{00}=4\sin^2\Theta\,K(1+4V)$ and the derived Yukawa potential would change. On the data side, the predicted rotation curve $v^2(R)=(GM/R)(1+\beta e^{-R/d}(1+R/d))$ has a distinctive shape, so high-resolution rotation-curve data in the transition region would reveal whether the scale $d$ is fixed or mass-dependent.

Watch

Extended reading notes

Core claim

The central claim is that the flavor vacuum of mixed Dirac neutrinos is not gravitationally empty: its semiclassical energy-momentum tensor has $p=0$, matching the equation of state of dust and cold dark matter, and in a static spherically symmetric weak-field metric it sources a correction to the Newtonian potential of the form $V(R)=-(GM/R)(1+\beta e^{-R/d})$. The derivation starts from the observation that all spatial components of the flavor-vacuum stress tensor vanish because the mixing generator commutes with spatial-derivative bilinears, leaving only $T_{00}$. In the weak-field limit, using flat-space modes rescaled by $1+\tfrac{3}{2}V(R)$, the energy density becomes $T_{00}=4\sin^2\Theta\,K(1+4V(R))$, and solving the Poisson equation with this source yields the Yukawa solution. Applied to galaxies, this potential produces flat rotation curves and a baryonic mass–rotation velocity relation consistent with observed galaxy samples.

Load-bearing premise

The argument depends on assuming that neutrino wave modes in the curved spacetime of a galaxy are the flat-space modes multiplied by a factor that depends on the gravitational potential; this keeps the modes normalized, but the paper does not prove that these modes satisfy the curved-space version of the neutrino wave equation.

Editorial extensions

If this is right

  • Flat rotation curves of spiral galaxies would follow from the additional Yukawa term without invoking any new particle species.
  • The model produces a baryonic mass–rotation velocity relation of the observed form, with fitted parameters consistent across spiral and gas-dominated galaxy samples.
  • The flavor-vacuum energy density scales as $\sin^2\Theta$ and vanishes without mixing, so the effect is a genuine consequence of neutrino flavor rotation.
  • The ultraviolet scale $\Lambda$ of the flat-space condensate controls the length scale $d$ of the Yukawa correction, linking particle-physics parameters to galactic dynamics.
  • The same formalism generalizes from static spherical symmetry to broader classes of spacetimes, so the dark-matter-like equation of state may also hold in cosmological settings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct numerical check would be to solve the curved-space radial Dirac system for the rescaled-mode ansatz; if the residual is not first-order small, the exact form of $T_{00}$ could differ from $4\sin^2\Theta\,K(1+4V)$, though the qualitative Yukawa shape might survive.
  • If the effect is real, the same flavor-vacuum condensate should also gravitate in other weakly curved environments, such as galaxy clusters, so searching for the characteristic Yukawa scale $d$ in cluster lensing would be a natural extension.
  • The derivation leaves the absolute normalization $K$ dependent on an ultraviolet cutoff; fixing $K$ from measured rotation curves would turn the fit into a prediction relating the neutrino mass difference and mixing angle to galactic dynamics.
  • Because the effect uses only ordinary neutrino mixing, it could coexist with a particle dark-matter component and would change the expected mass of the dark-matter halo needed to fit galaxy dynamics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper claims that the flavor vacuum state of two-flavor neutrino mixing in curved spacetime has a semiclassical energy-momentum tensor with the equation of state of dust (p = 0), and that in a weak-field static spherically symmetric spacetime this vacuum source produces a Yukawa correction to the Newtonian potential, V(R) = -(GM/R)(1 + beta e^{-R/d}), which can account for flat rotation curves and the baryonic Tully-Fisher relation. The argument has three parts: an algebraic proof that all spatial components of the flavor-vacuum energy-momentum tensor vanish; a weak-field calculation of T00 using rescaled flat-space Dirac modes; and phenomenological fits to galaxy data in two scenarios for the ultraviolet cutoff or the mixing parameter. The algebraic part is clean, but the weak-field derivation is not: the rescaled modes do not solve the curved-space Dirac equation, and the rotation-curve and Tully-Fisher applications rest on further invalid approximations.

Significance. If the derivation were correct, the proposal would be significant because it would source galactic dark-matter phenomenology from standard-model neutrino mixing without new particles. The paper has genuine strengths: Section III's proof that the spatial components of the flavor-vacuum energy-momentum tensor vanish is concise and appears correct; the galaxy samples are realistic; and the fitting procedure is transparent. Nevertheless, the central result, Eq. (56), and the derived Yukawa potential are not established, and the rotation-curve and Tully-Fisher applications rely on an invalid large-distance expansion and an arbitrary definition of a0. As it stands, the paper's main phenomenological claim is unsupported.

major comments (5)
  1. [§IV.B, Eqs. (52)–(56)] Substituting Phi = h Phi0, Psi = h Psi0 with h = 1 + 3V/2 into the radial Dirac system (23) does not yield an O(V^2) identity. With f = 1 + 2V, g = 1 - 2V, sqrt(g) ≈ 1 - V, sqrt(g/f) ≈ 1 - 2V, and sqrt(g)T ≈ -V'/2, the two equations leave first-order residuals approximately (2E - M)V Phi0 - V' Psi0 and -(M + 2E)V Psi0 - V' Phi0. These are O(V) and O(V'), not O(V^2), so the modes of Eq. (55) are not approximate solutions of the curved-space Dirac equation. Equation (54) verifies only orthonormality of the rescaled modes; completeness is asserted without proof. Since Eq. (56) is derived from these modes, the Yukawa source is not established.
  2. [§IV.B, passage after Eq. (55)] The statement that 'the potential is sufficiently weak that no q states, i.e. with E_L <= M_L, are formed' is an unproved assumption. The radial system (23) with an attractive potential can support bound states with E_L < M_L, and the q-integral in Eq. (42) would contribute to T00 if such states exist. This omission is load-bearing because Eq. (56) uses only the p-integral and drops the q-contribution without justification.
  3. [§V, Eqs. (59)–(61)] The parameters of the Yukawa potential are not predicted by the neutrino physics in the paper. In Eq. (61), beta is introduced as a free dimensionless parameter, while d = 1/(2 sqrt(alpha)) is fixed by choosing the cutoff Lambda0 to reproduce the Milky Way value d_MW of ref. [102]. In scenario 1, the cutoff is further allowed to scale as Lambda = Lambda0 (M/M_MW)^nu with nu fitted; in scenario 2, beta is postulated to scale as M^{-1/2} with beta0 fitted. No relation to neutrino masses, the mixing angle, or a fundamental cutoff is derived, so the galaxy fits test a two-parameter phenomenological curve rather than a prediction from neutrino mixing.
  4. [§V.A, Eqs. (63)–(65)] Equation (63) gives v^2(R) = (GM/R)[1 + beta e^{-R/d}(1 + R/d)], which for R >> d tends to GM/R, not to a constant. The 'expansion at first order' leading to Eq. (64) is valid only for R << d, yet it is then extrapolated to large R to obtain Eq. (65). Thus the claimed flatness of the rotation curve is an artifact of an invalid limit; the Yukawa potential of Eq. (61) does not produce asymptotically flat rotation curves for a point mass.
  5. [§V.B, Eqs. (66)–(68)] The baryonic Tully-Fisher relation is not derived: Eq. (66) is evaluated at the arbitrarily chosen point R = d to define a0 in Eq. (67), whereas v^4(R) is not constant in R. Replacing a0 by this chosen value converts the definition into a fit, so Eq. (68) and the subsequent fits in Tables III and IV do not constitute a prediction. The procedure is therefore not a test of the QFT mechanism.
minor comments (5)
  1. [Footnote 4] The phrase 'There is no such modes in the Minkowskian limit' should read 'There are no such modes in the Minkowskian limit'.
  2. [§IV.A, Eq. (49)] The quantity K is called a 'spacetime constant', but it depends on the ultraviolet cutoff Lambda through Eq. (50); this should be stated explicitly at the point where K is introduced.
  3. [§V.A, Tables III and IV] No uncertainties or goodness-of-fit statistics are reported for the fitted values of beta, nu, and beta0. With two free parameters and no error bars, it is difficult to assess the quality or robustness of the fits.
  4. [§V.B, scenario 1] The cutoff value Lambda0 ≈ 1.5425 keV is chosen solely to reproduce d_MW, but the paper does not explain why this scale, which is far below typical neutrino mass differences, should be related to neutrino mixing parameters.
  5. [§IV.B, after Eq. (59)] The integration constant in Eq. (59) is discarded as an 'irrelevant additive constant', but the corresponding constant in the vacuum energy density acts like a cosmological constant term and its backreaction on the metric is not addressed anywhere in the paper.

Circularity Check

2 steps flagged · score 6.0 of 10

The Yukawa potential step itself is not circular, but the claimed derivation of the baryonic Tully-Fisher relation reduces by construction to an imposed scaling, and the galactic scale d is imported from a self-cited fit; the assumed curved-space Dirac modes remain an acknowledged unproved gap.

  1. fitted input called prediction [Section V.B, Eqs. (67)-(69), scenario 2 and Table IV]
    "There is however a second possibility for the baryonic Tully-Fisher relation to be reproduced with a constant ultraviolet cutoff and an appropriate scaling of β ∼ M^{−1/2}. Exquisitely from the point of view of QFT this latter possibility is more appealing. ... 2. Universal d and universal cutoff, varying β, with β = β0 (M/M_MW)^(−1/2) and β0 a parameter to be determined."

    The claimed consequence v^4_FLAT = G M a0 is not derived from neutrino mixing: the proportionality v^4 ∝ M is forced by choosing β ∝ M^{-1/2}. Inserting β = β0(M/M_MW)^{-1/2} into Eq. (67), a0 = 4GMβ²e^{-2}/d², makes a0 independent of M, so v^4 = GM a0 ∝ M identically. The parameter β0 is then fitted (Table IV) rather than computed. The phrase 'for the baryonic Tully-Fisher relation to be reproduced' shows the scaling was selected to manufacture the target relation; the paper's introductory claim to 'derive the baryonic Tully-Fisher relation' therefore rests on an assumption equivalent to the result.

  2. self citation load bearing [Section V.A after Eq. (65) and Section V.B, scenario 1]
    "According to the best fit values presented in [102] both β and d depend on the galaxy under consideration, in particular βMW = 0.4, dMW = 0.74 kpc and βM31 = 0.37, dM31 = 0.52 kpc. ... Here Λ0 is picked to reproduce the value dMW = 0.74 kpc found in [102] and equals Λ0 ≃ 1.5425 keV, while ν is an exponent to be determined."

    The length scale d = 1/(2√α) of the claimed flavor-vacuum Yukawa term is not fixed by neutrino masses and mixing; it is fixed by choosing the ultraviolet cutoff Λ0 specifically so that the model reproduces dMW = 0.74 kpc. The source [102] shares an author (S. Capozziello) with the present paper and is itself a fit of the same Yukawa potential to the Milky Way and M31 rotation curves. The galactic scale of the 'neutrino mixing effect' is therefore imported from a self-cited fit to the very phenomenon the paper claims to explain, and it is load-bearing for every subsequent galactic fit in Tables III and IV.

full rationale

The general dust equation-of-state result (Section III) is self-contained: Eq. (11) algebraically shows spatial bilinears are invariant under the mixing generator, giving T_jk = 0 and hence p = 0. The weak-field chain (Eqs. (51)-(59)) is also not circular in the narrow sense: the paper writes a Poisson equation with the flavor-vacuum source and solves it for V(R), obtaining the Yukawa form; the unknown constant C is then calibrated via β. The major mathematical gap is the Dirac-mode ansatz of Section IV.B: Eqs. (55) only preserve the normalization integral (Eq. (54)), and the assertion that they form an orthonormal and complete set, together with the assumption that no q-states form, is not proved; substituting the ansatz into Eq. (23) leaves O(V) residuals. However, an unproved ansatz is a correctness gap, not a circular reduction, and I do not count it in the score. What does raise the score is the galactic phenomenology: the strength β is 'freely specifiable' (Eq. (61)) and fitted to the data, the scale d is imported from a self-cited Milky Way fit by choosing Λ0, and the baryonic Tully-Fisher relation is reproduced only after imposing β ∝ M^{-1/2} (or Λ ∝ M^{-1/2} with fitted ν), which makes v^4 ∝ M by construction. The paper's conclusion admits the limitation: 'the analysis may be refined beyond the approximations used, aiming at exact solutions to the Dirac equations and the full non-linear Poisson equation.' Because the central Yukawa derivation is not equivalent to its inputs but two 'derived' galactic relations reduce to fitted or imported inputs, the overall circularity score is 6.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central derivation relies on standard QFT in curved spacetime plus several choices specific to this paper: an ansatz for the Dirac modes that is not verified against the equation of motion, a UV cutoff chosen to match galactic data, and per-galaxy and global fit parameters beta and nu. No new particles are introduced; the flavor vacuum is an existing concept.

free parameters (4)
  • beta = 0.433 (spirals), 0.417 (gas), 0.427 (combined) in scenario 1; beta0 = 0.414 or 2.6e-8 in scenario 2 depending on cutoff
    Dimensionless strength of the Yukawa correction in Eq. (61). It is fitted to the baryonic Tully-Fisher data in Section V.B and is not determined by neutrino masses or mixing angles.
  • nu = -0.521 (spirals), -0.517 (gas), -0.516 (combined)
    Exponent governing the scaling of the UV cutoff with baryonic mass in scenario 1. It is fitted to the same baryonic Tully-Fisher data, and the value near -1/2 is what is needed to reproduce the observed v^4 proportional to M relation.
  • UV cutoff Lambda0 = 1.5425 keV
    Chosen so that the Milky Way Yukawa length d_MW = 0.74 kpc from ref. [102] is reproduced. The physical origin of this cutoff is not specified, and it directly sets the Yukawa scale d.
  • Integration constant C = C = -GM beta per galaxy
    Arbitrary per-galaxy constant in Eq. (59) that sets the overall strength of the Yukawa term. It is equivalent to fitting beta for each galaxy.
assumptions (5)
  • domain assumption Quantum field theory in curved spacetime with a global foliation and tetrad formulation for Dirac fields on globally hyperbolic manifolds.
    Section II, Eqs. (1)-(4). This is the standard framework assumed without derivation.
  • domain assumption Normal ordering with respect to the mass vacuum isolates the pure mixing contribution to the flavor-vacuum energy-momentum tensor.
    Section II, footnote 2 and Eq. (8). The subtraction is a regularization convention that defines the physical quantity.
  • ad hoc to paper The rescaled flat-space modes Phi = (1 + 3V/2) Phi0 and Psi = (1 + 3V/2) Psi0 form a complete orthonormal set for the weakly curved Dirac field without solving Eq. (23).
    Section IV.B, Eqs. (52)-(55). Only normalization preservation is checked, not the Dirac equation, yet the modes are declared complete and used to compute T00.
  • ad hoc to paper The weak potential is such that no q-states with E_L <= M_L are formed.
    Section IV.B, paragraph after Eq. (55). This excludes bound-state modes that would change the form of T00.
  • ad hoc to paper The UV cutoff Lambda in Eq. (50) is a free regulator, allowed in scenario 1 to vary with galaxy mass as Lambda proportional to M^nu.
    Section V.B, scenario 1. The cutoff is not derived from the theory; its value and mass dependence are fitted to reproduce the baryonic Tully-Fisher relation.
invented entities (1)
  • None
    purpose: No new particles, forces, or dimensions are introduced
    The flavor vacuum is an existing concept in quantum field theory of neutrino mixing; the paper assigns it a new gravitational role but does not postulate a new entity.

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Cite this review

Pith. "Pith review of Missing matter in galaxies as a neutrino mixing effect." pith.science (2026). https://pith.science/paper/MU4GE3YK

@misc{pith2026241117319,
  author       = {Pith},
  title        = {Pith review of: Missing matter in galaxies as a neutrino mixing effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MU4GE3YK}},
  note         = {Machine review of arXiv:2411.17319}
}
read the original abstract

We show that, in the framework of quantum field theory in curved spacetime, the semiclassical energy-momentum tensor of the neutrino flavor vacuum fulfills the equation of state of dust and cold dark matter. We consider spherically symmetric spacetimes, and we demonstrate that, within the weak field approximation, the flavor vacuum contributes as a Yukawa correction to the Newtonian potential. This corrected potential may account for the flat rotation curves of spiral galaxies. In this perspective, neutrino mixing could contribute to dark matter

Figures

Figures reproduced from arXiv: 2411.17319 by the authors.

Figure 1
Figure 1. FIG. 1. (color online) Plots of the best fit (solid blue line) for Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (color online) Plots of the best fit (solid blue line) for Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (color online) Logarithmic scale plot of the best fit (solid blue line) for Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

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Works this paper leans on

111 extracted references · 72 canonical work pages

  1. [102]

    Szmytkowski, Journal of Mathematical Chemistry 42, 397-413 (2007)

    R. Szmytkowski, Journal of Mathematical Chemistry 42, 397-413 (2007)

    work page 2007

  2. [1]

    Here Λ 0 is picked to reproduce the valuedM W= 0.74 kpc found in [102] and equals Λ 0 ≃ 1.5425 keV, while ν is an exponent to be determined

    Universal β and varying cutoff, with Λ = Λ0 M MM W ν . Here Λ 0 is picked to reproduce the valuedM W= 0.74 kpc found in [102] and equals Λ 0 ≃ 1.5425 keV, while ν is an exponent to be determined. The results are presented in Fig. 1 with the best fit values summarized in Table III. The data agrees with β ≃ 0.42 and ν ≃ −0.52, in accordance with the expecte...

  3. [2]

    The results are presented in Figs

    Universal d and universal cutoff, varying β, with β = β0 M MM W − 1 2 and β0 a parameter to be determined. The results are presented in Figs. 2 and 3 with the best fit values summarized in table IV. For Λ = Λ 0, β0 ≃ 0.42, while it is much smaller for larger cutoff, β0 ≃ 2.6 × 10−8 for Λ = ΛEW = 246 GeV. It should be noted that Eq. (67) is insensitive to ...

  4. [3]

    de Bernardis et al., Nature, 404, 955 (2000)

    P. de Bernardis et al., Nature, 404, 955 (2000)

    2000

  5. [4]

    Spergel et al

    D.N. Spergel et al. ApJS, 148, 175 (2003)

    2003

  6. [5]

    Dodelson et al., ApJ, 572, 140 (2002)

    S. Dodelson et al., ApJ, 572, 140 (2002)

    2002

  7. [6]

    Szalay et al., ApJ, 591, 1 (2003)

    A.S. Szalay et al., ApJ, 591, 1 (2003)

    2003

  8. [7]

    Durrer, R., Maartens, R. (2008). General Relativity and Gravitation, 40(2-3), 301-328

    2008

Show all 111 references
  1. [8]

    P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003)

    2003

  2. [9]

    Riess et al., ApJ, 607, 665 (2004)

    A.G. Riess et al., ApJ, 607, 665 (2004)

    2004

  3. [10]

    Trimble, Annual Review of Astronomy and Astrophysics 25.1, pp

    V. Trimble, Annual Review of Astronomy and Astrophysics 25.1, pp. 425–472 (1987)

    1987

  4. [11]

    Corbelli and P

    E. Corbelli and P. Salucci, Monthly Notices of the Royal Astronomical Society 311.2, pp. 441-447 (Jan. 2000)

    2000

  5. [12]

    V. C. Rubin, Jr. Ford W. K., Astrophysical Journal 159, p. 379 (Feb. 1970)

    1970

  6. [13]

    V. C. Rubin, Jr. Ford W. K. and N. Thonnard, Astrophysical Journal 238, pp. 471–487 (June 1980)

    1980

  7. [14]

    Clowe et al., ApJ 649, 2 (2006)

    D. Clowe et al., ApJ 649, 2 (2006)

    2006

  8. [15]

    Aghanim et al., A & A 641, A6 (2020)

    N. Aghanim et al., A & A 641, A6 (2020)

    2020

  9. [16]

    Joyce et al., Phys

    A. Joyce et al., Phys. Rep. 568, pp. 1–98 (2015)

    2015

  10. [17]

    Bertone, D

    G. Bertone, D. Hooper, J. Silk, Phys. Rep. 405, issues 5–6, pp. 279–390 (2005)

    2005

  11. [18]

    P. F. de Salas and A. Widmark, Rep. Prog. Phys. 84, 104901 (2021)

    2021

  12. [19]

    History of dark matter

    G. Bertone and D. Hooper, “History of dark matter”, Rev. Mod. Phys. 90, 045002 (2018)

    2018

  13. [20]

    Bergstr¨ om, Rep

    L. Bergstr¨ om, Rep. Prog. Phys.63, 793 (2000)

    2000

  14. [21]

    Roszkowski, E

    L. Roszkowski, E. M. Sessolo and S. Trojanowski, Rep. Prog. Phys. 81, 066201 (2018)

    2018

  15. [22]

    Klasen, M

    M. Klasen, M. Pohl and G. Sigl, Prog. Part. Nucl. Phys. 85, pp. 1–32 (2015)

    2015

  16. [23]

    Conrad and O

    J. Conrad and O. Reimer, Nat. Phys. 13, 224 (2017)

    2017

  17. [24]

    Schumann, J

    M. Schumann, J. Phys. G: Nucl. Part. Phys. 46, 103003 (2019)

    2019

  18. [25]

    Berlin, Phys

    A. Berlin, Phys. Rev. Lett. 117, 231801 (2016)

    2016

  19. [26]

    Necib, M

    L. Necib, M. Lisanti and V. Belokurov, Astrophys. J 874, 3 (2019)

    2019

  20. [27]

    Mayet et al., Phys

    F. Mayet et al., Phys. Rep. 627, 1 (2016)

    2016

  21. [28]

    R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, pp. 1791-1797 (1977)

    1977

  22. [29]

    Arvanitaki et al., Phys

    A. Arvanitaki et al., Phys. Rev. D 81 (2010)

    2010

  23. [30]

    Raffelt, Stars as Laboratories for Fundamental Physics, University of Chicago Press, Chicago, ill, USA, 1996

    G. Raffelt, Stars as Laboratories for Fundamental Physics, University of Chicago Press, Chicago, ill, USA, 1996

    1996

  24. [31]

    Astrophysical axion bounds

    G. G. Raffelt, “Astrophysical axion bounds”, in Axions, Lecture Notes in Physics Vol. 741, pp. 51–71, Springer, Berlin, Germany, 2008

    2008

  25. [32]

    Capolupo, G

    A. Capolupo, G. Lambiase, A. Quaranta, S. M. Giampaolo, Phys. Lett. B 804, 135407 (2020)

    2020

  26. [33]

    De Martino, T

    I. De Martino, T. Broadhurst, S. H. H. Tye, T. Chiueh, H.Y. Schive, R. Lazkoz, Phys. Rev. Lett. 119 (22), 221103 (2017)

    2017

  27. [34]

    Capolupo, S

    A. Capolupo, S. M. Giampaolo and A. Quaranta, Eur. Phys. J. C 81, 1116 (2021)

    2021

  28. [35]

    Capolupo, I

    A. Capolupo, I. De Martino, G. Lambiase and An. Stabile, Phys. Lett. B 790, pp. 427–435 (2019)

    2019

  29. [36]

    De Martino, T

    I. De Martino, T. Broadhurst, S. H. H. Tye, T. Chiueh, H. Y. Schive, R. Lazkoz, Galaxies 6 (1), 10 (2018)

    2018

  30. [37]

    Aune et al., Phys

    S. Aune et al., Phys. Rev. Lett. 107, no. 26, article ID 261302 (2011)

    2011

  31. [38]

    Capolupo, G

    A. Capolupo, G. Lambiase, G. Vitiello, Adv. High En. Phys., 2015, 826051 (2015)

    2015

  32. [39]

    Addazi, S

    A. Addazi, S. Capozziello, Q. Gan, G. Lambiase and R. Samanta, [arXiv:2411.09042 [astro-ph.CO]] (2024)

    2024 arXiv

  33. [40]

    T. D. Lee and C. N. Yang, Phys. Rev. 104, 254 (1956)

    1956

  34. [41]

    I. Y. Kobzarev, I.Y., L.B. Okun and I. Y. Pomeranchuk, Sov. J. Nucl. Phys. 3, 6, 837-841 (1966)

    1966

  35. [42]

    S. I. Blinnikov and M. Y. Khlopov, Sov. J. Nucl. Phys. 36, 472 (1982)

    1982

  36. [43]

    Berezhiani, Int

    Z. Berezhiani, Int. J. Mod. Phys. A 19, 3775-3806 (2004)

    2004

  37. [44]

    H. M. Hodges, Phys. Rev. D 47, 456-459 (1993)

    1993

  38. [45]

    Foot, Int

    R. Foot, Int. J. Mod. Phys. A 29, 1430013 (2014)

    2014

  39. [46]

    Capolupo, G

    A. Capolupo, G. Pisacane, A. Quaranta and F. Romeo, Phys. Dark Univ. 46, 101688 (2024). 17

    2024

  40. [47]

    Krasznahorkay et al., Phys

    A.J. Krasznahorkay et al., Phys. Rev. Lett. 116, 042501 (2016)

    2016

  41. [48]

    Krasznahorkay et al., J

    A.J. Krasznahorkay et al., J. Phys. Confer. Ser. 1056, 012028 (2018)

    2018

  42. [49]

    Feng et al., Phys

    J.L. Feng et al., Phys. Rev. Lett. 117, 071803 (2016)

    2016

  43. [50]

    Feng et al., Phys

    J.L. Feng et al., Phys. Rev. D 95, 035017 (2017)

    2017

  44. [51]

    Capolupo, A

    A. Capolupo, A. Quaranta, R. Serao, The impact of the X17 boson on particle physics anomalies: muon anomalous magnetic moment, Lamb shift, W mass, Phys. of Dark Univ., in press (2024)

    2024

  45. [52]

    Jungman, M

    G. Jungman, M. Kamionkowski and K. Griest, Phys. Rep. 267.5, pp. 195–373 (1996)

    1996

  46. [53]

    Boyarsky, M

    A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens and O. Ruchayskiy, Prog. Nucl. Part. Phys. 104, pp.1-45 (2019)

    2019

  47. [54]

    Capozziello and M

    S. Capozziello and M. De Laurentis, Phys. Rep. 509, Issues 4-5, pp. 167-321 (2011)

    2011

  48. [55]

    Capriolo, Int

    M. Capriolo, Int. J. Geom. Meth. Mod. Phys. 19, no.10, 2250159 (2022)

    2022

  49. [56]

    Capozziello, M

    S. Capozziello, M. Capriolo and G. Lambiase, Int. J. Geom. Meth. Mod. Phys. 20, no.10, 2350177 (2023)

    2023

  50. [57]

    Y. F. Cai, S. Capozziello, M. De Laurentis and E. N. Saridakis, Rept. Prog. Phys. 79 (2016) no.10, 106901

    2016

  51. [58]

    Fukuda et al., Phys

    (Super-Kamiokande Collaboration) Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998)

    1998

  52. [59]

    Abe et al., Phys

    (Double Chooz Collaboration) Y. Abe et al., Phys. Rev. Lett. 108, 131801 (2012)

    2012

  53. [60]

    F. P. An et al., Phys. Rev. Lett. 108, 171803 (2012)

    2012

  54. [61]

    Abe et al., Phys

    (T2K Collaboration) K. Abe et al., Phys. Rev. D 88, 032002 (2013)

    2013

  55. [62]

    S. M. Bilenky and B. Pontecorvo, Phys. Rep. 41.4, pp. 225-261 (1978)

    1978

  56. [63]

    S. M. Bilenky and S. T. Petcov, Rev. Mod. Phys. 59, pp. 671-754 (1987)

    1987

  57. [64]

    Alfinito, M.Blasone, A.Iorio, G.Vitiello, Phys

    E. Alfinito, M.Blasone, A.Iorio, G.Vitiello, Phys. Lett. B 362, 91 (1995)

    1995

  58. [65]

    Blasone, A

    M. Blasone, A. Capolupo and G. Vitiello, Phys. Rev. D 66, 025033 (2002)

    2002

  59. [66]

    Blasone, A

    M. Blasone, A. Capolupo, S. Capozziello, S. Carloni, G. Vitiello, Phys. Lett. A 323, pp. 182–189 (2004)

    2004

  60. [67]

    Ji and Y

    C.-R. Ji and Y. Mishchenko, Phys. Rev. D 65, 096015 (2002)

    2002

  61. [68]

    Capolupo, S

    A. Capolupo, S. M. Giampaolo and A. Quaranta, Phys. Lett. B 820, 136489 (2021)

    2021

  62. [69]

    Capolupo and A

    A. Capolupo and A. Quaranta, J. Phys. G 50, 055003 (2023)

    2023

  63. [70]

    Capolupo, S

    A. Capolupo, S. M. Giampaolo, B. C. Hiesmayr, G. Lambiase and A. Quaranta, J. Phys G 50, 025001 (2023)

    2023

  64. [71]

    Capolupo, S

    A. Capolupo, S. M. Giampaolo, G. Lambiase and A. Quaranta, Universe 2020, 6(11), 207 (2020)

    2020

  65. [72]

    Buchm¨ uller,Neutrinos, Grand Unification and Leptogenesis , arXiv:hep-ph/0204288v2 (2002)

    W. Buchm¨ uller,Neutrinos, Grand Unification and Leptogenesis , arXiv:hep-ph/0204288v2 (2002)

    2002 arXiv

  66. [73]

    Tanabashi et al

    M. Tanabashi et al. (Particle Data Group), Neutrinos in Cosmology , Phys. Rev. D 98, 030001 (2018)

    2018

  67. [74]

    Betti et al

    M.G. Betti et al. (PTOLEMY collaboration), JCAP 07, 047 (2019)

    2019

  68. [75]

    D. B. Kaplan, A. E. Nelson, N. Weiner, Phys. Rev. Lett. 93, 091801 (2004)

    2004

  69. [76]

    Fardon, A

    R. Fardon, A. E. Nelson, N. Weiner, JCAP 10, 005 (2004)

    2004

  70. [77]

    H. P. Nilles, M. Peloso and L. Sorbo, JHEP04 2001 (2001)

    2001

  71. [78]

    Grossman and H

    Y. Grossman and H. J. Lipkin, Phys. Rev. D 55, 2760 (1997)

    1997

  72. [79]

    Capolupo, G

    A. Capolupo, G. De Maria, S. Monda, A. Quaranta and R. Serao, Universe 2024, 10(4), 170 (2024)

    2024

  73. [80]

    Piriz, M

    D. Piriz, M. Roy and J. Wudka, Phys. Rev. D 54, 1587 (1996)

    1996

  74. [81]

    C. Y. Cardall and G. M. Fuller, Phys. Rev. D 55, 7960 (1997)

    1997

  75. [82]

    Capolupo, G

    A. Capolupo, G. Lambiase and A. Quaranta, Phys. Rev. D 101, 095022 (2020)

    2020

  76. [83]

    Capolupo, S

    A. Capolupo, S. Carloni and A. Quaranta, Phys. Rev. D 105, 105013 (2022)

    2022

  77. [84]

    Capolupo, A

    A. Capolupo, A. Quaranta and R. Serao, Symmetry 2023, 15(4), 807 (2023)

    2023

  78. [85]

    Parker, Phys

    L. Parker, Phys. Rev. 183, 1057 (1969) and Phys. Rev. D 3, 346 (1971)

    1969

  79. [86]

    Capolupo, Adv

    A. Capolupo, Adv. High En. Phys. 2018, 9840351 (2018)

    2018

  80. [87]

    Capolupo, S

    A. Capolupo, S. Capozziello, G. Vitiello, Phys. Lett. A 373, pp. 601–610 (2009)

    2009

  81. [88]

    Quantum fields in curved space

    N. D. Birrell and P. C. Davies, “Quantum fields in curved space”, Cambridge University Press (1982)

    1982

  82. [89]

    Capolupo, S

    A. Capolupo, S. Capozziello, G. Vitiello, Phys. Lett. A 363, 53 (2007)

    2007

  83. [90]

    Capolupo, Adv

    A. Capolupo, Adv. High Energy Phys. 2016, 8089142 (2016)

    2016

  84. [91]

    Capolupo and A

    A. Capolupo and A. Quaranta, J. Phys. G 51, 105202 (2024)

    2024

  85. [92]

    Capolupo and A

    A. Capolupo and A. Quaranta, Phys. Lett. B 840, 137889 (2023)

    2023

  86. [93]

    Quantum field theory in curved spacetime: quantized fields and gravity

    L. Parker and D. Toms, “Quantum field theory in curved spacetime: quantized fields and gravity”, Cambridge University Press (2009)

    2009

  87. [94]

    Capolupo and A

    A. Capolupo and A. Quaranta, Phys. Lett. B 839, 137776 (2023)

    2023

  88. [95]

    Quantum field theory in curved space–time

    L. H. Ford, “Quantum field theory in curved space–time”, 9th Jorge Andre Swieca Summer School: Particles and Fields, arXiv gr-qc/9707062, pp. 345–388 (1997)

    1997 arXiv

  89. [96]

    Capolupo, A

    A. Capolupo, A. Quaranta and P. A. Setaro, Phys. Rev. D 106, 043013 (2022)

    2022

  90. [97]

    Capolupo, S

    A. Capolupo, S. M. Giampaolo, G. Lambiase and A. Quaranta, Eur. Phys. J. C 80, 423 (2020)

    2020

  91. [98]

    Milgrom, Astrophys

    M. Milgrom, Astrophys. J. 270, 365 (1983)

    1983

  92. [99]

    Milgrom and R

    M. Milgrom and R. H. Sanders, Astrophys. J. Lett. 599, L25 (2003)

    2003

  93. [100]

    Benisty and S

    D. Benisty and S. Capozziello, Phys. Dark Univ. 39 (2023), 101175

    2023

  94. [101]

    Egorov, M

    V. Egorov, M. Smolyakov and I. Volobuev, Class. Quantum Grav. 41, 045002 (2024)

    2024

  95. [103]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications Inc., New York, (1965)

    1965

  96. [104]

    D’Agostino, K

    R. D’Agostino, K. Jusufi and S. Capozziello, Eur. Phys. J. C 84, 386 (2024)

    2024

  97. [105]

    P. J. McMillan, Monthly Notices of the Royal Astronomical Society 414, 3, 2446-2457 (2011)

    2011

  98. [106]

    Jusufi, G

    K. Jusufi, G. Leon and A. D. Millano, Phys. Dark Univ. 42, 101318 (2023)

    2023

  99. [107]

    V. F. Cardone and S. Capozziello, Mon. Not. Roy. Astron. Soc. 414 (2011), 1301. 18

    2011

  100. [108]

    Stabile and S

    A. Stabile and S. Capozziello, Phys. Rev. D 87 (2013) no.6, 064002

    2013

  101. [109]

    S. S. McGaugh, The Astrophysical Journal 632, 859 (2005)

    2005

  102. [110]

    Capozziello, P

    S. Capozziello, P. Jovanovi´ c, V. Borka Jovanovi´ c and D. Borka, JCAP2017, 044 (2017)

    2017

  103. [111]

    Bernal, S

    T. Bernal, S. Capozziello, J. C. Hidalgo and S. Mendoza, Eur. Phys. J. C 71 (2011), 1794

    2011

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