Dynamical Resolution of the Cosmic Coincidence Problem in Non-Interacting Holographic Dark Energy via Einstein-Cartan Torsion

We investigate the cosmic coincidence problem in non-interacting holographic dark energy with the Hubble radius as the infrared cutoff in Einstein-Cartan gravity. In general relativity, this cutoff gives a dust-like equation of state in the non-interacting case, whereas interacting models require a phenomenological dark sector coupling and yield a constant density ratio. We show that the Einstein-Cartan torsion scalar $\Phi$, compatible with the cosmological principle, with the self-consistent scaling behavior $\Phi\sim a^{-3}$, makes the density ratio $r\equiv \rho_m/\rho_X$ dynamical even when the phenomenological interaction term is absent, $Q=0$. The same torsion contribution shifts the equation of state for holographic dark energy toward negative values, allowing cosmic acceleration, and realizes the observed order-unity density ratio within the weak torsion regime without tuning the holographic free parameter. Thus, Einstein-Cartan torsion provides a geometric mechanism that replaces the phenomenological dark sector interaction and offers a dynamical resolution of the cosmic coincidence problem.