Theoretical deduction of the Hubble law beginning with a MoND theory in context of the ${\Lambda}$FRW-Cosmology

TL;DR

This paper derives the Hubble law and estimates the universe's age using a modified gravity theory with an Inverse Yukawa Field, linking large-scale dynamics with cosmological models and providing insights into dark energy.

Contribution

It introduces the IYF as a non-local modification to gravity, deriving the Hubble law and universe age within a MoND framework in the context of $\Lambda$FRW cosmology.

Findings

Derived Hubble law as v = (4 π G / c) r at large scales

Estimated universe's age as approximately 11 billion years

Obtained a maximum Hubble constant of about 86 km/s/Mpc

Abstract

We deducted 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 result we connected the dynamics of astronomical objects at great scale with the Friedmann-Robertson-Walker ($\Lambda$FRW) model. From the corresponding formalism, the Hubble law can be expressed as v = (4 $\pi$ [G]/c)r, which was derivated by evaluating the IYF force at distances much greater than 50Mpc, giving a maximum value for the expansion rate of the universe of $H_0=86,31$, 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 a large scale of baryonic matter. Additionally, we calculated the age of the universe as 11Gyr, in agreement with recent measurements of the age of the white dwarfs in the solar neighborhood.