A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters

Alexander Munson

doi:10.33187/jmsm.1763817

A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters

Abstract

In this paper, the de Broglie matter wave model of inverse scattering of neutrinos in the cosmic neutrino background (CNB) by thermalized electrons in galaxy superclusters is presented and examined. Theoretical aspects of the model, such as the relativistic frequency shift of the neutrino in the rest frame of the thermalized electron, are given. An extension of the model at the galactic level is given by the resultant change in the observed power spectrum of the up-scattered neutrinos in the CNB passing through galactic clusters integrated along the line of sight of the observer. Applications of the de Broglie matter wave model of CNB neutrino scattering, such as an energy scale estimate of the collision between relic neutrinos and thermalized electrons at a scale consistent with the mean thermal energy of electrons in most galaxy supercluster surveys, are presented. Methodologies that utilize statistical distributions of the meta-aggregate excitations of primordial neutrinos to estimate the overall energy of the Big Bang and to examine the evolution of the expanding Universe are discussed. Further cosmological implications of the model on the ratio of the mean matter density of the Universe $\rho_{GM}$ to the ordinary baryon and dark matter constant $\Omega_{M}$, which forecasts the fate of the expanding Universe, are presented. Future research directions, such as the instrumentation designs of space-based neutrino detectors (SBNDs) to measure CNB neutrino scattering by the model, are also proposed. The primary audience of the paper is cosmologists, astrophysicists, and mathematical modelling academicians.

Keywords

Big Bang theory, Cosmological evolution models, de Broglie matter-waves, Energy scale, Neutrino scattering

References

[1] E. Hubble, A relation between distance and radial velocity among extra-galactic nebulae, Proc. Nat. Acad. Sci., 15(3) (1929), 168-173. https://doi.org/10.1073/pnas.15.3.168
[2] A. Penzias, R.Wilson, A measurement of excess antenna temperature at 4080Mc/s, Astrophys. J., 142(1) (1965), 419-421. https://doi.org/10.1086/148307
[3] A. Riess, A. Filippenko, P. Challis, et al., Observational evidence from supernovae for an accelerating Universe and a cosmological constant, Astron. J., 116(3) (1998), 2267-2281. https://doi.org/10.1086/300499
[4] G. Marinello, R. Clowes, L. Campusano, et al., Compatibility of the large quasar groups with the concordance cosmological model, Astron. J., M. Not. R. Astron Soc., 461(3) (2016), 3-19. https://doi.org/10.1093/mnras/stw1513
[5] Q. Guo, S. D. M. White, Galaxy growth in the concordance $\Lambda$CDM cosmology, M. Not. R. Astron Soc., 384(1) (2008), 2-10. https://doi.org/10.1111/j.1365-2966.2007.12619.x
[6] D. Spergel, L. Verde, E. Komatsu, et al., First year Wilkinson anisotropy probe (WMAP) observations: determination of cosmological parameters, Astron. J. Suppl. Ser., 148(1) (2003), 175-232.
[7] R. Croft, D. Weinberg, M. Bolte, et al., Toward a precise measurement of matter clustering: $L_{y\alpha}$ forest data at redshifts 2-4, Astron. J., 581(1) (2002), 20-52. https://doi.org/10.1086/344099
[8] L. Page, M. R. Nolta, C. Barnes, et al., First year Wilkinson anisotropy probe (WMAP) observations: interpretation of the TT and TE angular power spectrum peaks, Astron. J. Suppl. Ser., 148(1) (2003), 233-241. https://doi.org/10.1086/377224
[9] P. de Bernadis, P. A. R. Ade, J. J. Bock, et al., A flat Universe from high-resolution maps of the cosmic microwave background radiation, Nat., 404 (2000), 955-959. https://doi.org/10.1038/35010035
[10] M. S. Turner, The road to precision cosmology, Annu. Rev. Nuclear. Part. Sci., 72 (2022), 1-35. https://doi.org/10.1146/annurev-nucl-111119-041046

[11] G. W. Gibbons, S. W. Hawking, S. T. C. Siklos, The Very Early Universe, Cambridge University Press, Cambridge, 1982.
[12] B. Ryden, Introduction to Cosmology, Cambridge University Press, Cambridge, 2017.
[13] Y. H. Chen, M. Fishbach, D. Holz, A two percent Hubble constant measurement from standard sirens within five years, Nat., 562 (2018), 545-547. https://doi.org/10.1038/s41586-018-0606-0
[14] R. A. Sunyaev, Ya. B. Zeldovich, Small-scale fluctuations of relic radiation, Astrophys. Space Sci., 7(1) (1970), 3-19.
[15] P. R. Philips, Calculation of the kinetic Sunyaev-Zeldovich effect from the Boltzmann equation, Astrophys. J., 455 (1995), 419-420.
[16] J. P. Hughes, K. Yamashita, Y. Okumura, et al., Isothermality of the gas in the Coma cluster, Astrophys. J., 327 (1988), 615-626.
[17] B. R. Safdi, M. Lisanti, J. Spitz, et al., Annual modulation of cosmic relic neutrinos, Phys. Rev. D, 90(4) (2014), Article ID 043001. https://doi.org/10.1103/PhysRevD.90.043001
[18] The KM3NeT Collaboration, S. Aiello, A. Albert, et al., Observation of an ultra-high energy cosmic neutrino with KM3NeT, Nature, 638 (2025), 376-382. https://doi.org/10.1038/s41586-024-08543-1
[19] H. T. Wong, H. B. Li, S. K. Lin, et al., Research program towards observation of neutrino-nucleus coherent scattering, Nucl. Phys. B. Proc. Suppl, 221(2011), 320-323. https://doi.org/10.1016/j.nuclphysbps.2011.09.024
[20] P. S. Barbeau, J. I. Collar, O. Tench, Large-mass ultra-low noise Germanium detectors: Performance and applications in neutrino and astroparticle physics, J. Cosmol. Astropart. Phys., 9 (2007), 9-29. 10.1088/1475-7516/2007/09/009
[21] S. J. Brice, R. L. Cooper, F. DeJongh, et al., A method for measuring coherent elastic neutrino-nucleus at far off-axis high-energy neutrino beam target, Phys. Rev. D, 89 (2014), Article ID 072004. https://doi.org/10.1103/PhysRevD.89.072004
[22] S. Adrian-Martinez, A. Albert, M. Andre, et al., Searches for point-like and extended neutrino sources close to the galactic centre using the ANTARES neutrino telescope, Astrophys. J. Lett., 786 (2014), Article ID L5. https://doi.org/10.1088/2041-8205/786/1/L5
[23] G. P. Thomson, A. Reid, Diffraction of cathode rays by a thin film, Nature, 119 (1927), Article ID 890.
[24] A. Zeilinger, R. Ghler, C. G. Shull, et al., Single and double-slit diffraction of neutrons, Rev. Mod. Phys., 60(4) (1988), 1067-1073. https://doi.org/10.1103/RevModPhys.60.1067
[25] M. Arndt, O. Nairz, J. Voss-Andreae, et al., Wave-particle duality of $C_{60}$ molecules, Nat., 401 (1999), 680-682. https://doi.org/10.1038/44348
[26] T. Alber, G. A. Petsko, D. Tsernoglou, Crystal structure of elastase-substrate complex at $-55^{\circ}C$, Nature, 263(5575) (1976), 297-300. https://doi.org/10.1038/263297a0
[27] A. Comastri, G. Setti, G. Zamorani, et al., The contribution of AGNs to the X-ray background, Astronom. Astrophys., 296(1) (1995), 241-255.
[28] M. J. Colbrook, X. Ma, P. F. Hopkins, et al., Scaling laws of passive-scalar diffusion in the interstellar medium, Mon. Not. R. Astron. Soc., 467(2) (2017), 2421-2429. https://doi.org/10.1093/mnras/stx261
[29] I. Koca, Analysis of Cauchy problems for variable-order derivatives with Mittag-Leffler kernel, Math. Model. Numer. Simul. Appl.,4(5) (2024), 64-78. https://doi.org/10.53391/mmnsa.1544150

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Alexander Munson ^*
0009-0000-6980-9762
United States

Early Pub Date

January 22, 2026

Publication Date

January 22, 2026

Submission Date

August 13, 2025

Acceptance Date

January 18, 2026

Published in Issue

Year 2026 Volume: 9 Number: 1

DOI

https://doi.org/10.33187/jmsm.1763817

IZ

https://izlik.org/JA24BJ74WF

APA

Munson, A. (2026). A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters. Journal of Mathematical Sciences and Modelling, 9(1), 1-12. https://doi.org/10.33187/jmsm.1763817

AMA

1.Munson A. A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters. Journal of Mathematical Sciences and Modelling. 2026;9(1):1-12. doi:10.33187/jmsm.1763817

Chicago

Munson, Alexander. 2026. “A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters”. Journal of Mathematical Sciences and Modelling 9 (1): 1-12. https://doi.org/10.33187/jmsm.1763817.

EndNote

Munson A (March 1, 2026) A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters. Journal of Mathematical Sciences and Modelling 9 1 1–12.

IEEE

[1]A. Munson, “A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters”, Journal of Mathematical Sciences and Modelling, vol. 9, no. 1, pp. 1–12, Mar. 2026, doi: 10.33187/jmsm.1763817.

ISNAD

Munson, Alexander. “A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters”. Journal of Mathematical Sciences and Modelling 9/1 (March 1, 2026): 1-12. https://doi.org/10.33187/jmsm.1763817.

JAMA

1.Munson A. A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters. Journal of Mathematical Sciences and Modelling. 2026;9:1–12.

MLA

Munson, Alexander. “A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters”. Journal of Mathematical Sciences and Modelling, vol. 9, no. 1, Mar. 2026, pp. 1-12, doi:10.33187/jmsm.1763817.

Vancouver

1.Alexander Munson. A Model to Calibrate the Expansion of the Universe by Thermalized Scattering of the Cosmic Neutrino Background in Galaxy Superclusters. Journal of Mathematical Sciences and Modelling. 2026 Mar. 1;9(1):1-12. doi:10.33187/jmsm.1763817