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Addressing the cosmological \(H_0\) tension by the Heisenberg uncertainty

Abstract

The uncertainty on measurements, given by the Heisenberg principle, is a quantum concept usually not taken into account in General Relativity. From a cosmological point of view, several authors wonder how such a principle can be reconciled with the Big Bang singularity, but, generally, not whether it may affect the reliability of cosmological measurements. In this letter, we express the Compton mass as a function of the cosmological redshift. The cosmological application of the indetermination principle unveils the differences of the Hubble-Lemaître constant value, \(H_0\), as measured from the Cepheids estimates and from the Cosmic Microwave Background radiation constraints. In conclusion, the \(H_0\) tension could be related to the effect of indetermination derived in comparing a kinematic with a dynamic measurement.

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References

  1. Riess, A.G., Casertano, S., Yuan, W., Macri, L.M., Scolnic, D.: Large Magellanic Cloud Cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond LambdaCDM. Astrophys. J. 876, 85 (2019)

    ADS  Article  Google Scholar 

  2. Aghanim, N., et al.: [Planck Collaboration], Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209v2 [astro-ph.CO] (2019)

  3. Verde, L., Treu, T., Riess, A.G.: Tensions between the early and the late universe. Nat. Astron. 3, 891 (2019)

    ADS  Article  Google Scholar 

  4. Benetti, M., Miranda, W., Borges, H.A., Pigozzo, C., Carneiro, S., Alcaniz, J.S.: Looking for interactions in the cosmological dark sector. J. Cosm. Astropart. Phys. 1912, 023 (2019)

    ADS  Article  Google Scholar 

  5. Graef, L.L., Benetti, M., Alcaniz, J.S.: Primordial gravitational waves and the H0-tension problem. Phys. Rev. D 99, 43519 (2019)

    ADS  Article  Google Scholar 

  6. Benetti, M., Graef, L.L., Alcaniz, J.S.: The \(H_0\) and \(\sigma _8\) tensions and the scale invariant spectrum. J. Cosm. Astropart. Phys. 1807, 066 (2018)

    ADS  Article  Google Scholar 

  7. Bernal, J.L., Verde, L., Riess, A.G.: The trouble with \(H_0\). J. Cosm. Astropart. Phys. 1610, 019 (2016)

    ADS  Article  Google Scholar 

  8. Kang, Y., Lee, Y.W., Kim, Y.L., Chung, C., Ree, C.H.: Early-type host galaxies of type Ia Supernovae. II. Evidence for luminosity evolution in Supernova cosmology. Astrophys. J. 889, 8 (2020)

    ADS  Article  Google Scholar 

  9. Abbott, B.P., et al.: Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016); Errata Corrige: 121, 122902(E) (2018)

  10. Will, C.M.: Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries. Phys. Rev. D 57, 2061 (1998)

    ADS  Article  Google Scholar 

  11. Aviles, A., Bravetti, A., Capozziello, S., Luongo, O.: Precision cosmology with Padé rational approximations: theoretical predictions versus observational limits. Phys. Rev. D 90, 043531 (2014)

    ADS  Article  Google Scholar 

  12. Capozziello, S., Ruchika, Sen, A.A.: Model independent constraints on dark energy evolution from low-redshift observations. Mon. Not. R. Astron. Soc. 484, 4484 (2019)

    ADS  Article  Google Scholar 

  13. Capozziello, S., D’Agostino, R., Luongo, O.: Extended gravity cosmography. Int. J. Mod. Phys. D 28, 1930016 (2019)

    ADS  MathSciNet  Article  Google Scholar 

  14. Tanabashi, M., and the Particle Data Group: Review of particle physics. Phys. Rev. D 98, 030001 (2018)

  15. Retinò, A., Spallicci, A.D.A.M., Vaivads, A.: Solar wind test of the de Broglie–Proca massive photon with Cluster multi-spacecraft data. Astropart. Phys. 82, 49 (2016)

    ADS  Article  Google Scholar 

  16. Williams, E.R., Faller, J.E., Hill, H.A.: New experimental test of Coulomb’s law: a laboratory upper limit on the photon rest mass. Phys. Rev. Lett. 26, 721 (1971)

    ADS  Article  Google Scholar 

  17. de Broglie, L.: Nouvelles Recherches sur la Lumière. Actualités Scientifiques et Industrielles, vol. 411. Hermann & \({\text{C}}^{\text{ ie }}\), Paris (1936)

  18. Stueckelberg, E.C.G.: Théorie de la radiation de photons de masse arbitrairement petite. Helv. Phys. Acta 30, 209 (1957)

    MathSciNet  MATH  Google Scholar 

  19. Boulware, D.G.: Renormalizeability of massive non-Abelian gauge fields: a functional integral approach. Ann. Phys. 56, 140 (1970)

    ADS  MathSciNet  Article  Google Scholar 

  20. Guedelman, E.: Gauge invariance and mass without spontaneous symmetry breaking. Phys. Rev. Lett. 43, 543 (1979)

    ADS  Article  Google Scholar 

  21. Scharff Goldhaber, A., Nieto, M.M.: Photon and graviton mass limits. Rev. Mod. Phys. 82, 939 (2010)

    ADS  Article  Google Scholar 

  22. Itzykson, C., Zuber, J.-B.: Quantum Field Theory. Dover Publications, Mineola (2012)

    MATH  Google Scholar 

  23. Bonetti, L., dos Santos Filho, L.R., Helayël-Neto, J.A., Spallicci, A.D.A.M.: Effective photon mass from Super and Lorentz symmetry breaking. Phys. Lett. B 764, 203 (2017)

    ADS  Article  Google Scholar 

  24. Bonetti, L., dos Santos Filho, L.R., Helayël-Neto, J.A., Spallicci, A.D.A.M.: Photon sector analysis of Super and Lorentz symmetry breaking: effective photon mass, bi-refringence and dissipation. Eur. Phys. J. C 78, 811 (2018)

    ADS  Article  Google Scholar 

  25. Nussinov, S.: Charge-nonconserving decays. Phys. Rev. Lett. 59, 2401 (1987)

    ADS  Article  Google Scholar 

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Acknowledgements

SC and MB acknowledge the Istituto Nazionale di Fisica Nucleare (INFN), sezione di Napoli, iniziative specifiche MOONLIGHT2 and QGSKY. ADAMS acknowledges the Erasmus+ programme for visiting the Università di Napoli, SC the Université d’Orléans and Campus France for the hospitality. Authors thank the referees and J. A. Helayël-Neto for precious suggestions which allowed to improve the paper.

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Correspondence to Salvatore Capozziello.

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Capozziello, S., Benetti, M. & Spallicci, A.D.A.M. Addressing the cosmological \(H_0\) tension by the Heisenberg uncertainty. Found Phys 50, 893–899 (2020). https://doi.org/10.1007/s10701-020-00356-2

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  • DOI: https://doi.org/10.1007/s10701-020-00356-2

Keywords

  • Heisenberg principle
  • Observational cosmology
  • Hubble-Lemaître constant