Foundations of Physics

, Volume 47, Issue 9, pp 1208–1228 | Cite as

Hubble Law: Measure and Interpretation

  • Georges PaturelEmail author
  • Pekka Teerikorpi
  • Yurij Baryshev


We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed: (1) improvement of observational means (ground-based radio and optical observations, space missions); (2) understanding of the biases that affect both distant and local determinations of the Hubble constant; (3) new theoretical and observational results. These circumstances encourage us to take a critical look at some facts and ideas related to the cosmological red-shift. This is important because we are probably on the eve of a new understanding of our Universe, heralded by the need to interpret some cosmological key observations in terms of unknown processes and substances.


Cosmology Distance scale Hubble constant Space expansion 



Y.B. thanks for support from the Saint-Petersburg State University research Project No. We are very grateful to our collaborators over many years Lucienne Gouguenheim, Gilles Theureau, Jean-Noël Terry, Chantal Petit and Mikko Hanski, and remember with admiration the late Lucette Bottinelli and Timo Ekholm. We want to sincerely thank referees for their valuable contributions.


  1. 1.
    Slipher, V.M.: On spectrographic observations of nebulae and clusters. PAAS. 4, 284 (1922)Google Scholar
  2. 2.
    Lemaître, G.: Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques. AASB. 47, 49 (1927)zbMATHGoogle Scholar
  3. 3.
    Lundmark, K.: The motions and distances of spiral nebulae. MNRAS 85, 865 (1925)ADSCrossRefGoogle Scholar
  4. 4.
    Hubble, E.: A relation between distance and radial velocity among extragalactic nebulae. Proc. Nat. Acad. Sci. 15, 168–173 (1929)ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    Maddox, J.: Dispute over scale of Universe. Nature 307, 313 (1984)ADSCrossRefGoogle Scholar
  6. 6.
    Giovanelli, R.: Less expansion more agreement. Nature 400, 111–112 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    Roberts, M.S.: The neutral Hydrogen content of late-type spiral galaxies. Astron. J. 67, 437 (1962)ADSCrossRefGoogle Scholar
  8. 8.
    Gouguenheim, L.: Neutral Hydrogen content of small galaxies. Astron. Astrophys. 3, 281 (1969)ADSGoogle Scholar
  9. 9.
    Tully, R.B., Fisher, R.: A new method for determining distances to galaxies. Astron. Astrophys. 54, 661 (1977)ADSGoogle Scholar
  10. 10.
    Teerikorpi, P.: Observational selection bias affecting the determination of the extragalactic distance scale. Ann. Rev. Astron. Astrophys. 35, 101–136 (1997)ADSCrossRefGoogle Scholar
  11. 11.
    Teerikorpi, P.: The inverse Tully-Fisher relation. Astro Lett. and Comm. 31, 263 (1995)ADSGoogle Scholar
  12. 12.
    Terry, J.N., Paturel, G., Ekholm, T.: Local velocity field from sosie galaxies : The Peeble’s model. Astron. Astrophys. 393, 57 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    Spaenhauer, A.M.: A systematic comparison of four methods to derive stellar space densities. Astron. Astrophys. 65, 313 (1978)ADSGoogle Scholar
  14. 14.
    Bottinelli, L., Gouguenheim, L., Paturel, G., Teerikorpi, P.: The Malmquist bias and the value of \(H_0\) from the Tully-Fisher Relation. Astron. Astrophys. 156, 157 (1986)ADSGoogle Scholar
  15. 15.
    Bottinelli, L., Gouguenheim, L., Paturel, G., Teerikorpi, P.: The Malmquist bias in the extragalactic distance scale : Controversies and misconceptions. Astrophys. J. 328, 4 (1988)ADSCrossRefGoogle Scholar
  16. 16.
    Lutz, T.E., Kelker, D.H.: On the Use of Trigonometric Parallaxes for the Calibration of Luminosity Systems: Theory. PASP 85, 573 (1973)ADSCrossRefGoogle Scholar
  17. 17.
    Feast, M.W., Catchpole, R.M.: The Cepheid period-luminosity zero-point from HIPPARCOS trigonometrical parallaxes. MNRAS 286, L1–L5 (1997)ADSCrossRefGoogle Scholar
  18. 18.
    Freedman, W.L. et al., Final results from the Hubble Space Telescope Key Project to measure the Hubble constant. Astrophys.J 553, 47-72Google Scholar
  19. 19.
    Beaton, R.L., Freedman, W.L., Madore, B.F., et al.: The Carnegie-Chicago Hubble Program I : A new approach to the distance ladder. Astrophys. J. 832, 2101 (2016)CrossRefGoogle Scholar
  20. 20.
    Teerikorpi, P.: Malmquist bias in a relation of the form \(M=a P+b\). Astron. Astrophys. 141, 407 (1984)ADSGoogle Scholar
  21. 21.
    Hamuy, M., Phillips, M.M., Suntzeff, N.B.: et al, The Hubble diagram of the Calan/Tololo Type Ia Supernovae and the value of \(H_0\). Astron. J. 112, 2398 (1996)ADSCrossRefGoogle Scholar
  22. 22.
    Riess, A.G., Filippenko, A.V., Challis, P., et al.: Observational evidence from supernovae for an acccelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)ADSCrossRefGoogle Scholar
  23. 23.
    Perlmutter, S., Aldering, G., Goldhaber, G., et al.: Measurement of \(\Omega \) and \(\Lambda \) from 42 high-red-shift supernovae. Astrophys J. 517, 565 (1999)ADSCrossRefGoogle Scholar
  24. 24.
    Bennett, C.L., Larson, D., Weiland, J.L., et al.: Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations : Final Maps and Results. Astrophys. J. Supl. 208, 20 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    Ade, P.A.R., Aghanin, N., Arnaud, M., et al.: Planck 2015 results. XIII. Cosmological parameters. Astron. Astrophys. 594, 15 (2016)CrossRefGoogle Scholar
  26. 26.
    Gieren, W., Fouqué, P., Gomez, M.: Cepheid period radius and period luminosity relations and the distance to the Large Magellanic Cloud. Astrophys. J. 496, 17 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    Benedict, G.F., Mc Arthur, B.E., Feast, M.W., et al.: Hubble space telescope fine guidance sensor parallaxes of Galactic Cepheid variable stars: period luminosity relation. Astron. J. 133, 1810 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    Herrnstein, J.R., Moran, J.M., Greenhill, L.J., et al.: A geometric distance to the galaxy NGC 4258 from orbital motions in a nuclear gas disk. Nature 400, 539 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    Hoffman, S.L., Riess, A.G., Macri, L.M., et al.: Optical identification of Cepheids in 19 host galaxies of Type Ia Supernovae and NGC 4258 with the Hubble space telescope. Astrophys. J. 830, 10 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    Riess, A.G., Macri, L.M., Hoffman, S.L., et al.: A 2.4% determination of the local value of the hubble constant. Astrophys. J. 826, 56 (2016)ADSCrossRefGoogle Scholar
  31. 31.
    Tully, R.B., Courtois, H.M., Dolphin, A.E., et al.: Cosmicflow-2: data. Astron. J. 146, 86 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    Teerikorpi, P.: Cluster population incompleteness and distances from the TF relation—theory and numerical example. Astron. Astrophys. 173, 39 (1987)ADSGoogle Scholar
  33. 33.
    Sandage, A.: Cepheids as distance indicators when used near their detection limit. PASP 100, 935 (1988)ADSCrossRefGoogle Scholar
  34. 34.
    Schechter, P.L.: Mass-to-light ratios for Elliptical galaxies. Astron. J. 85, 801 (1980)ADSCrossRefGoogle Scholar
  35. 35.
    Tully, R.B.: Origin of the Hubble constant controversy. Nature 334, 209 (1988)ADSCrossRefGoogle Scholar
  36. 36.
    Teerikorpi, P., Ekholm, T., Hanski, M.O., Theureau, G.: Theoretical aspects of the inverse Tully–Fisher relation as a distance indicator: incompleteness in \(logV_{max}\), the relevant slope, and the calibrator sample bias. Astron. Astrophys. 343, 713 (1999)ADSGoogle Scholar
  37. 37.
    Teerikorpi, P., Paturel, G.: Evidence for the extragalactic Cepheid distance bias from the kinematical distance scale. Astron. Astrophys. 381, L37–L40 (2002)ADSCrossRefGoogle Scholar
  38. 38.
    Madore, B.F., in From the Realm of the Nebulae to Populations of Galaxies, Eds. D’Onofrio, M., Rampazzo, R., Zaggia, S., Springer, New York, pp. 132 (2016)Google Scholar
  39. 39.
    Madore, B.F.: The period luminosity relation: IV—intrinsic relation and reddenings for the Large Magellanic Cloud Cepheids. Astrophys. J. 253, 575 (1982)ADSCrossRefGoogle Scholar
  40. 40.
    Van den Bergh, S.: The galaxies of the local group. JRAS of Canada 62, 145 (1968)ADSGoogle Scholar
  41. 41.
    Inno, L., Bono, G., Matsunaga, N.: The panchromatic view of the Magellanic Cloud from classical Cepheids I: distance, rddening and geometry. Astrophys. J. 832, 176 (2016)ADSCrossRefGoogle Scholar
  42. 42.
    Ekholm, T., Lanoix, P., Teerikorpi, P., et al.: Investigation of the local supercluster velocity field. Astron. Astrophys. 351, 827–833 (1999)ADSGoogle Scholar
  43. 43.
    Ekholm, T., Baryshev, Y., Teerikorpi, P., et al.: On the quiescence of the Hubble flow in the vicinity of the Local Group: A study using galaxies with distances from the Cepheid PL-relation. Astron. Astrophys. 368, L17–L20 (2001)ADSCrossRefGoogle Scholar
  44. 44.
    Karachentsev, I.D., et al.: The very local Hubble flow. Astron. Astrophys. 389, 812–824 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    Sandage, A.: The red-shift-distance relation. IX. Astrophys. J. 307, 1 (1986)ADSCrossRefGoogle Scholar
  46. 46.
    Paturel, G., Teerikorpi, P.: The extragalactic Cepheid bias: a new test using the Period–Luminosity–color relation. Astron. Astrophys 452, 423–430 (2006)ADSCrossRefGoogle Scholar
  47. 47.
    Lanoix, P., Garnier, R., Paturel, G., et al.: Extragalactic Cepheid database. Astron. Nachr. 320, 1 (1999)ADSCrossRefGoogle Scholar
  48. 48.
    Baryshev, Yu., Teerikorpi, P.: Fundamental Questions of Practical Cosmology. Springer, Berlin (2012)CrossRefGoogle Scholar
  49. 49.
    Baryshev, Y.V.: Paradoxes of the cosmological physics in the beginning of the 21-th century. In: Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects, pp. 297–307 (2015). arXiv:1501.01919
  50. 50.
    Harrison, E.R.: The red-shift-distance and velocity-distance laws. Astrophys. J. 403, 28 (1993)ADSCrossRefGoogle Scholar
  51. 51.
    Sanejouand, Y.H.: A simple Hubble like law in lieu of dark energy (2015). arXiv:1401.2919v6
  52. 52.
    de Sitter, W.: On Einstein’s theory of gravitation and its astronomical consequences. In: MNRAS. LXXVI. 9, 699 (1916)Google Scholar
  53. 53.
    de Sitter, W.: On Einstein’s theory of gravitation and its astronomical consequences II. In: MNRAS LXXVII. 2, 155 (1917)Google Scholar
  54. 54.
    de Sitter, W.: On Einstein’s theory of gravitation and its astronomical consequences III. In: MNRAS LXXVIII. 1, 3 (1917)Google Scholar
  55. 55.
    Eddington, A.S.: The Mathematical Theory of Relativity, p. 161. Cambridge University Press, Cambridge (1923)zbMATHGoogle Scholar
  56. 56.
    Tolman, R.C.: On the astronomical implications of the de Sitter line element of the universe. Astrophys. J. 69(245), 1929 (1929)Google Scholar
  57. 57.
    Sandage, A.: Galaxies and the Universe. The University of Chicago Press, Chicago (1975)Google Scholar
  58. 58.
    Sandage, A.: Astronomical problems for the next three decades. In: Mamaso, A., Munch, G. (eds.) Key Problems in Astronomy and Astrophysics. Cambridge University Press, Cambridge (1995)Google Scholar
  59. 59.
    Sandage, A.: The Tolman surface brightness test for the reality of the expansion, V. Provenance of the test and a new representation of the data for three remote Hubble space telescope galaxy clusters. Astron. J. 139, 728 (2010)ADSCrossRefGoogle Scholar
  60. 60.
    Sandage, A.: The change of red-shift and apparent luminosity of galaxies due to the deceleration of the expanding universes. ApJ 136, 319 (1962)ADSCrossRefGoogle Scholar
  61. 61.
    Liske, J., Grazian, A., Vanzella, E., et al.: Cosmic dynamics in the era of extremely large telescopes. Mon. Not. R. Astron. Soc. 386, 1192 (2008)ADSCrossRefGoogle Scholar
  62. 62.
    Baryshev, Y.V.: The hierarchical structure of metagalaxy a review of problems, Reports of Special Astrophysical Observatory of the Russian Academy of Sciences 14, p. 24 (1981) (English translation: 1984 Allerton Press)Google Scholar
  63. 63.
    Baryshev, Y.V.: Field fractal cosmological model as an example of practical cosmology approach, in Practical Cosmology, Proceedings of the International Conference held at Russian Geographical Society, 23-27 June, 2008, Vol. 2, p. 60 (2008). arXiv:0810.0162
  64. 64.
    Lopez-Corredoira, M.: Tests of the expansion of the Universe (2015). arXiv:1501.01487
  65. 65.
    Sandage, A., Reindl, B., Tammann, G.: The linearity of the cosmic expansion field from 300 to 30,000 km s-1 and the bulk motion of the local supercluster with respect to the cosmic microwave background. Astrophys. J. 714, 1441 (2010)ADSCrossRefGoogle Scholar
  66. 66.
    Teerikorpi, P., Hanski, M., Theureau, G., et al.: The radial space distribution of KLUN-galaxies up to 200 Mpc: incompleteness or evidence for the behavior predicted by fractal dimension 2? Astron. Astrophys. 334, 395 (1998)ADSGoogle Scholar
  67. 67.
    Sylos Labini, F.: Inhomogeneous universe. Class. Quant. Grav. 28, 4003 (2011)Google Scholar
  68. 68.
    Tekhanovich, D.I., Baryshev, Y.V.: Global Structure of the Local Universe according to 2MRS Survey; ISSN 1990-3413, Astrophys. Bull., vol. 71, No. 2, pp. 155–164 (2016). arXiv: 1610.05206
  69. 69.
    Baryshev, Y.V.: Two fundamental cosmological laws of the Local Universe, Proceedings of the International Conference, Cosmology On Small Scales, Local Hubble Expansion and Selected Controversies in Cosmology, Prague, September 2124, 2016, Edited by Krǐzek, M., Dumin, Y.V.: Institute of Mathematics, Czech Academy of Sciences, Prague, pp. 9 22 (2016) arXiv:1610.05943
  70. 70.
    Wiens, E., Nevsky, A.Yu., Schiller, S.: Resonator with ultra-high stability as a probe for equivalence-principle-violating physics (2016). arXiv: 1612.01467V1
  71. 71.
    Landau, L.D, Lifschitz, E.M.: Theory of fields, Mir Ed., Moscow (1970)Google Scholar
  72. 72.
    Kopeikin, S.: Celestial Ephemerides in an expanding universe. Phys. Rev. D 86, 064004 (2012)ADSCrossRefGoogle Scholar
  73. 73.
    Kopeikin S.: Local gravitational physics of the Hubble expansion, Eur. Phys. J. Plus 130, p. 11 (2015). arXiv:1407.6667
  74. 74.
    Zwicky, F.: On the masses of nebulae and of clusters of nebulae. Astrophys. J. 86, 217 (1937)ADSCrossRefzbMATHGoogle Scholar
  75. 75.
    Milgrom, M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365 (1983)ADSCrossRefGoogle Scholar
  76. 76.
    Bekenstein, J.: Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Phys. Rev. D70, 083509 (2004)ADSGoogle Scholar
  77. 77.
    Blanchet, L.: Gravitational polarization and the phenomenology of MOND. Class. Quant. Gravity 24, 3529 (2007)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  78. 78.
    Guth, A.H.: Inflationary universe: a possible solution to the horizon and flatness problem. Phys. Rev. D 23, 347 (1981)ADSCrossRefGoogle Scholar
  79. 79.
    Peebles, P.J.E.: Principles of Physical Cosmology. Princeton University Press, Princeton (1993)Google Scholar

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Observatoire de LyonRetired from Universite Claude-BernardSaint-Genis LavalFrance
  2. 2.Department of Physics and Astronomy, Tuorla ObservatoryUniversity of TurkuPiikkiöFinland
  3. 3.Department of AstronomySt. Petersburg State UniversitySt.PetersburgRussia

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