In this review article, the electromagnetic coupling constant (fine structure), a microscopic dimensionless constant is connected to the macroscopic world using a corrected Valev’s proposed general solution for the mass dimension expression suggesting a link between the evolution of fundamental constants and cosmological parameters, like the cosmological constant. From the corrected and modified mass dimension expression M=mpγ1/2 (where mp is the Planck mass and γ = 4.4702596×10121 is a large dimensionless quantity defined as a quantum cosmological dimensionless constant), we calculate the total mass of ordinary matter in the universe in agreement with that found by the Planck(2018) collaboration and the Lambda CDM. In section six, we connect the fine structure constant to the cosmological parameters (the present root mean square matter fluctuation averaged over a sphere of radius 8h-1Mpc, the baryon density, the dark energy density and the reduced Hubble dimensionless parameter).In the results, the S8 tension is calculated and found to be in agreement with the recently observed CMB satellite value. A modification of the Einstein constant in the field equations also connects the fine structure constant and the cosmological parameters from which a new calculation of the S8 tension without the amplitude of the mass fluctuations is derived. Also In the results, exact equation of the Dirac large number 6.686×1060 has been found, connecting cosmological parameters and Planck units. Thus a precise formulation and evidence of Dirac large number hypothesis and fine structure constant has been found, connecting the microscopic worlds and the macroscopic worlds.