The One Inch Equation of the Universe: On the Same Origin of Quantum Physics and Gravity From Einstein Field Equations and Vacuum Energy Density Scale Formalism

It has been a long time to reconcile quantum physics and general relativity. To date, no globally accepted theory has been proposed to explain all physical observations. In this work, we reformulated the Einstein Field Equations (EFE) in terms of the Cosmological constant and energy density using the vacuum energy formalism. The proposed equation can be transformed into Maxwell equations in electrodynamics fields with a reduction in the background curvature. From the proposed unified equation we proved that the Cosmological constant follows a square law, that is; the Cosmological constant is proportional to the square of the MOND acceleration and the Planck mass .  When this result was connected to the calculations of  in the LambdaCDM, the following were the findings of the study:

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 We found out that the widely popularized MOND cosmological relationships are wrong. Our calculations gives a true relation.

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The mass of ordinary matter in the observable universe is calculated without using the critical density, volume or diameter of the Universe. The results we get agrees with the recent findings by Planck  unit who uses a critical density  and volume of the universe. 

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 We proved that the fine structure constant is related to the present root-mean-square matter fluctuation , the baryon density parameter , the density parameter and the reduced Hubble parameter. 

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 The exact equation of the large number  has been found, connecting cosmological parameters and Planck units. Thus, a precise formulation and evidence of Dirac Large Number Hypothesis has been found, connecting the micro world and the macro world.

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 We discovered a final equation that connects the Cosmological constant to the MOND acceleration and the Hubble constant into one Equation

•Our Unified equation also implies a vacuum energy density of dark energy for Planck mass sized particles accelerating with a constant MOND acceleration with a force equals to  Planck mass times MOND acceleration. The resulting vacuum energy value is proportional to the square of the MOND acceleration of the square of the Planck mass and  is in good agreement with the observed Planck (2015b) collaboration vacuum energy density of the Universe.