The Cosmological Constant Potential: a resolution to the Hubble tension via the cosmological sound horizon

The cosmological constant term can be seen as a constant potential for a (scalar) field. In this viewpoint, at late times, the field is stopped rolling and behaves as a cosmological constant ($w=-1$). While at the early universe, its kinetic term can be dominant and behaves as a stiff fluid ($w=+1$). This new phase lowers the cosmological sound horizon by increasing the Hubble parameter for very high redshifts. Consequently, the lower cosmological sound horizon results in the higher Hubble constant at the present time. This early phase ends before the photon decoupling, so we do not expect any new physics after the last scattering surface. We checked this model in the presence of (reduced) CMB, BAO's and $H_0$ datasets and could show the Hubble tension is fully relieved.