A Coherent Quantum Cosmology resolves the main cosmical enigma: Large Number correlations, dark matter, baryon density, vacuum energy. This is obtained from a non-reductionism analysis of data, and taking account of the Eddington's Fundamental theory and the non-Doppler cosmic oscillations with period tcc = 9600.606(12) s. The absence of Doppler effect (apart dephasages) induces the Tachyonic Principle: the world is divided in the c-visible part and a weakly interacting tachyonic one. In a gravitational Hydrogen Molecule, the Coherence Principle (identifying the ratio energy/h to an unifying frequency) gives the redshift (or Hubble) radius compatible with cT, where T ≈ 13.80(4) Gyr is the standard so-called Universe age. This model introduces an external Grandcosmos, considered as the source of the microwave background, the lacking element of the steady-state cosmology, and is tied to the vacuum energy, explaining its relative density about 10^120. In the critical Universe, classical and quantum energies egalise, in a new application of the Coherence Principle, and the Eddington's Number 136 × 2^256 of hydrogen atoms gives a baryon energy density 0.045 = (3/10)^2/2 related to the black matter one 3/10. With t_eF ≡ ħƛ_e^3/G_F the electron Fermi time, a c-free analysis defines a time 2t_cc²/t_eF, again compatible with T, confirming this is not any age but a fundamental period (Cycling Principle). In a Galilean critical steady-state Universe, the Coherent Principle applies a third time with the kinetic and potential energies equalised with the Eddington's one. The corresponding density is 3/10, resolving an unsolvable mystery of mainstream cosmology: the black energy density, compatible with the density 7/10. This Eddington model is shown to corresponds to a gravitational deuterium atom. This triple concordance, confirmed by many (40 or so) other correlations giving our proposal for TU = R_U/c, calls for an unification of the two major cosmologies; the Primordial Big Bang is then toppled in favor of the Permanent (13.812 Gyr Cycling) Vibrating Universe (t_U ≈ 0.838 10^-103 s), with a predicted value 70.79 km s-1 Mpc^-1 for the invariant recession constant, connected plausibly with a matter-antimatter scanned oscillation, resolving the antimatter and parity violation dilemma.