Holographic dark energy in Einstein-Cartan spin cosmology

We show that, in Einstein-Cartan theory, the torsion scalar modifies the dust-like equation of state of non-interacting holographic dark energy with the Hubble radius as the infrared cutoff, enabling late-time cosmic acceleration within the low-redshift domain of validity, which is not realized in the corresponding model in general relativity. Using the same holographic dark energy background, we further derive the torsion-induced modification of the cosmic distance duality relation, $d_L=d_A(1+z{)}^2(1+\eta )$. In the late-time universe, the magnitude of the deviation parameter, $\mathrm{\mid }\eta \mathrm{\mid }$, is small but non-vanishing, reflecting the cumulative effect of torsion along the light-propagation path.