In this versionV2 Universe`s age goes down 14.3Gyr This work presents the first application of the Dark Matter by Quantum Gravitation (DMbQG) theory to the study of the dark matter (DM) at cosmological scales. In the section 2 are introduced the Friedmann equations using the DMbQG theory, a key feature of this approach is the explicit separation between baryonic matter density and dark matter density. It is remarkable how in the DMbQG framework is demonstrated using the second Friedmann equation and the cosmological conservation equation that the effective DM density is a half of the physical DM one. This theoretical finding has several successful consequences studied in the sections 3 and 4. Also in this section, it is calculated the transition between the decelerating- accelerating eras, according to the DMbQG theory and the ΛCDM model. The theoretical calculus are tested with other published results. In the section 3, it is calculated the current cosmologic deceleration parameter by the two theoretical frameworks, being tested this calculus with other published results. Also it is studied the cosmological deceleration function depending on the z red-shift according to the two frameworks, yielding two quite different functions that could be tested by the recent results of the DESI project. In the section 4, the Universe`s age is calculated first within the standard ΛCDM model and subsequently using the DMbQG framework. A central result is that the age integral obtained with DMbQG is approximately 12.5% larger than that derived from ΛCDM. This difference allows for consistency with the Hubble constant measured by the PANTHEON project, based on Type Ia supernovae , with Hu2080 = 73.5 km /s/ Mpc, yielding an age of 14.3 Gyr. In contrast, applying this same value within ΛCDM leads to an age of 12.8 Gyr, in tension with the oldest known astrophysical objects. Consequently, ΛCDM relies on the Planck Collaboration value, Hu2080 = 67.4 km /s/ Mpc, which gives an age of 13.85 Gyr.Given that the SHOES or PANTHEON+ projects provide a more direct measurement of the present-day expansion rate, while the Planck value is inferred from early-Universe data (cosmic microwave background), the former may better represent the current Hubble parameter. The Hubble tension remains one of the major open problems in cosmology, and this work suggests that the DMbQG framework may offer a partial resolution by reconciling a higher Hu2080 value with a consistent estimate of the Universe’s age.