Theoretical Deduction of the Hubble Law Beginning with a MoND Theory in Context of the ΛFRW-Cosmology


We deduced the Hubble law and the age of the Universe, through the introduction of the Inverse Yukawa Field (IYF), as a non-local additive complement of the Newtonian gravitation (Modified Newtonian Dynamics). As a result, we connected the dynamics of astronomical objects at great scale with the Friedmann-Robertson-Walker ΛFRW) model. From the corresponding formalism, the Hubble law can be expressed as = (4π[G]/c)r, which was derived by evaluating the IYF force at distances much greater than 50 Mpc, giving a maximum value for the expansion rate of the universe of H0(max≈ 86.31 km·s-1Mpc-1, consistent with the observational data of 392 astronomical objects from NASA/IPAC Extragalactic Database (NED). This additional field (IYF) provides a simple interpretation of dark energy as the action of baryonic matter at large scales. Additionally, we calculated the age of the universe as 11 Gyr, in agreement with recent measurements of the age of the white dwarfs in the solar neighborhood.

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Falcon, N. and Aguirre, A. (2014) Theoretical Deduction of the Hubble Law Beginning with a MoND Theory in Context of the ΛFRW-Cosmology. International Journal of Astronomy and Astrophysics, 4, 551-559. doi: 10.4236/ijaa.2014.44051.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Hubble, E. (1929) A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae. Proceedings of the National Academy of Sciences, 15, 168-173.
[2] Lemaitre, G. (1927) A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocity of Extra-Galactic Nebulae. Annales de la Société Scientifique de Bruxelles, 47, 49-59.
[3] Riess, A. G., et al.(1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 116, 1009-1038.
[4] Perlmutter, S., et al. (1999) Measurements of Ω and Λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 517, 565-586.
[5] Freedman, W. and Madore, B. (2010) The Hubble Constant. Annual Review of Astronomy and Astrophysics, 48, 673-710.
[6] Browne, P.F. (1962) The Case for an Exponential Redshift Law. Nature, 193, 1019-1021.
[7] Segal, I.E., Nicoll, J.F., Wu, P. and Zhou, Z. (1993) Statistically Efficient Testing of the Hubble and Lundmark Laws on IRAS Galaxy Samples. The Astrophysical Journal, 411, 465-484.
[8] Strauss, M. and Koranyi, D. (1993) Tests of the Hubble Law from the Luminosity Function of IRAS Galaxies. arXiv:astro-ph/9308028
[9] Choloniewski, J. (1995) New Test for the Hubblelaw. arXiv:astro-ph/9504035
[10] Pascual-Sánchez, J.-F. (2000) A Generalized Linear Hubble Law for an Inhomogeneous Barotropic Universe. arXiv:gr-qc/0010076
[11] Liu, J.M. (2005) Modified Hubble Law, the Time-Varying Hubble Parameter and the Problem of Dark Energy. arXiv:physics/0507018 [physics.gen-ph]
[12] Sorrell, W.H. (2009) Misconceptions about the Hubble Recession Law. Astrophysics and Space Science, 323, 205-211.
[13] Sanejouand, Y.H. (2014) A Simple Hubble-Like Lawin Lieu of Dark Energy. arXiv:1401.2919 [astro-ph.CO]
[14] Falcón, N. (2013) Modification of the Newtonian Dynamics in ΛFRW-Cosmology an Alternative Approach to Dark Matter and Dark Energy. Journal of Modern Physics, 4, 10-18.
[15] Gundlach, J.H. (2005) Laboratory Tests of Gravity. New Journal of Physics, 7, 205.
[16] Milgrom, M. (1983) A Modification of the Newtonian Dynamics: Implications for Galaxies. The Astrophysical Journal, 270, 371-389.
[17] Falcón, N. (2011) MoND with Einstein’s Cosmological Term as Alternative to Dark Matter. Revista Mexicana de Astronomía y Astrofísica (Serie de Conferencias), 40, 11-12.
[18] Turyshev, S.G. and Toth, V.T. (2010) The Pioneer Anomaly. Living Reviews in Relativity, 13, 4.
[19] Sandage, A. (1958) Currents Problems in the Extragalactic Distance Scale. The Astrophysical Journal, 127, 513-526.
[20] Freedman, W., Madore, B.F., Gibson, B.K., Ferrarese, L., Kelson, D.D., Sakai, S., et al. (2001) Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant. The Astrophysical Journal, 553, 47-72.
[21] Bonamente, M., Joy, M.K., LaRoque, S.J., Carlstrom, J.E., Reese, E.D. and Dawson, K.S. (2006) Determination of the Cosmic Distance Scale from Sunyaev-Zel’dovich Effect and Chandra X-Ray Measurements of High-Redshift Galaxy Clusters. The Astrophysical Journal, 647, 25-54.
[22] Bennett, C., Larson, D., Weiland, J.L., Jarosik, N., Hinshaw, G., Odegard, N., et al. (2012) Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results. The Astrophysical Journal Supplement Series, 208, 20.
[23] Ade, P.A.R., Aghanim, N., Alves, M.I.R., Armitage-Caplan, C., Arnaud, M., Ashdown, M., et al. (2013) Planck 2013 Results. I. Overview of Products and Scientific Results. arXiv:1303.5062 [astro-ph.CO]
[24] Blakeslee, J., Lucey, J., Barris, B., Hudson, M. and Tonry, J. (2001) A Synthesis of Data from Fundamental Plane and Surface Brightness Fluctuation Surveys. Monthly Notices of the Royal Astronomical Society, 327, 1004-1020.
[25] Freedman, W. and Turner, M. (2003) Colloquium: Measuring and Understanding the Universe. Review of Modern Physics, 75, 1433-1447.
[26] Tremblay, P.E., Kalirai, J.S., Soderblom, D.R., Cignoni, M. and Cummings, J. (2014) White Dwarf Cosmochronology in the Solar Neighborhood. arXiv:1406.5173 [astro-ph.SR]
[27] Wang, S., Li, X. and Li, M. (2010) Revisit of Cosmic Age Problem. Physical Review D, 82, 103006.

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