Following in the footsteps of Max Planck, through the path of dimensional analysis, this study reveals the factor ξ =1,5457109×1011 which turns out to be omnipresent in cosmology, at all scales. This factor also appears in the form ξ4, as the ratio between the Coulomb energy and the gravitational energy, acting on an electron-positron pair, separated by a unit distance. This same factor reveals, through several independent paths, a cosmic and constant length: L = 2483 Gyl. In addition to the valuable tool offered by dimensional analysis, this study uses the mass unit "electron" which allows to compare dimensionless ratios with masses expressed in the same unit. The study indicates that Newton’s constant G, is determined with the parameters [M, L, T] of the electron and the factor ξ4. Via the factor ξ8 and the standard photon density, ρph = 4.1073×108 u / m^3, the study predicts the mass density ρ = 8.953389×10-10 J/ m^3. The application of the Friedmann-Lemaitre equation, reveals: Ho = 72.7411 km s-1 Mpc-1 = 2.360126×10-18 s-1; the age of the Universe, 13.44 Gy; the critical density ρc = 8.953386×10-10 J/ m^3 < ρ = 8.953389×10-10 J/ m³. These results are close to the results obtained by the WMAP 1 space probe, namely: 13.77 Gy; Ho = 73±3 km s-1 Mpc-1 = (2.35±0.10)×10-18 s-1. However, they are in disagreement with the results of the Planck 2018 mission: Ho = 67.4±0.4 km s-1 Mpc-1 = (2.18±0.01)×10-18 s-1. This study also reveals what could be likened to a cosmic "string" of length L and Planck section, whose volume is equal to the Compton volume of the electron.