This work presents the first application of the Dark Matter by Quantum Gravitation (DMbQG) theory to the study of dark matter (DM) at cosmological scales. In Section 2.1, the first Friedmann equation is introduced within the DMbQG framework. A key feature of this approach is the explicit separation between baryonic matter density and dark matter density. It is shown that, in this theory, the dark matter density evolves with the cosmological scale factor, a, following a power-law exponent of −2.5, in contrast to the ΛCDM model, where total matter density is not differentiated and scales as a with exponent -3.In Section 2.2, the second Friedmann equation and the cosmological conservation equation are presented. From the latter, the equation-of-state parameter w is derived for baryonic matter, dark matter, and dark energy. A novel result of this work is that, for dark matter, w = −1/6, which implies that its effective density is one-half of its physical density.In Section 3, the age of the Universe 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 11.5% larger than that derived from ΛCDM. This difference allows for consistency with the Hubble constant measured by the SHOES project, based on Type Ia supernovae in the local Universe, with Hu2080 = 73 km/s /Mpc, yielding an age of 14.7 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 method provides 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.