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

Abstract

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 v = (4 π[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 H 0 (max ) ≈ 86.31 km ·s -1 Mpc -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.