Decaying coupled Fermions to curvature and the $H_0$ tension

A formulation of cosmology driven by fermions $\psi$ is studied. Assumption of condensation for the spinor field simplifies the homogeneous solution of the Dirac equations and connects the spinor field with the scale parameter of the universe. With coupling between the Einstein term and spinor field, the possibility for a late time interaction emerges. In that way, the early universe agrees with $\Lambda$CDM model, but for the late universe the new integrating term dominates. From late time expansion data we obtain the $H_0$ from the SH0ES experiment. The data include the Pantheon Type Ia supernova, Quasars, Gamma Ray Bursts (for the Hubble diagram), cosmic chronometers and Byron Acoustic Oscillations. The decaying coupling reveals the capabilities of the scenario and makes it a good candidate for the description of nature. The tension can be reduced even further by including the local measurement of the Hubble constant.Comment: 5 pages, 2 figure