Simulations relating the Big-Bang-chronology to primordial quanta incrementing in number and elongating into CMB, suggested a quantum dependent-expansion based in parametric down-conversion (PDC). The PDC-dependent increase in the number of photons, by uniformly emerging and aggregating, when measure along the cosmos radius, yields per Mpc the Hubble’s constant value. Seeking to elucidate the correspondence between quantum-microscopic and macroscopic scalar-levels, their interaction was idealized by assuming that a quantum of space-time could be represented as an adiabatic Schrödinger’s box. Conjugation of the time-independent equation allowed a 3D-visual description of the intra- or inter-relationship between energy and space for a PDC-turnover. A chain of PDC turnover events, by conforming steps of lower and lower dissipative potential, operate a quasi-open thermodynamic system. Hence, allowing that at each of the sequence of PDC turnovers, the product, two photons of twice wavelength, do not accumulate, because in turn these become substrates for subsequent turnovers. The schematic representation of this process in a Schrödinger’s box, allowed predicting a photon-division transition as a two-peak wave. To analyze a theoretical bridge between gravitational independent sequences of PDC process, that by incrementing photon number and by their self-dimensioning expansion shows best-fit with the data obtain by astronomical observation. It is widely accepted that the increment in the universe volume could be related to the energy axis from Planck limit to present CMB. This has been idealized as a dissipative potential, of frequency decreasing in function of expanding Schrödinger’s boxes. This could become integrated as a dissipative potential, conforming a continuum of decreasing frequency density.