Preliminary test of cosmological models in the scale-dependent scenario

In the present work, we study for the first time a scale--dependent gravitational theory in a cosmological context in a matter--dominated era. In particular, starting from the Einstein Hilbert action with cosmological constant assuming scale--dependent couplings, we derive the corresponding effective Friedmann equations for the model and we solve them. We analyse in detail our results by comparing them with observational $\Lambda$CDM data as well as the very well-known running vacuum models. Finally, we have provided, in figures, the evolution of the Hubble parameter respect to the redshift as well as the gravitational coupling respect to the Hubble parameter and they show an agreement with the current observations.