Non-interacting holographic dark energy with Torsion via Hubble Radius

We reconstruct a holographic dark energy model within a Friedmann cosmology incorporating torsion scalar, assuming no interaction between dark energy and dark matter. Setting the Hubble radius as an infrared (IR) cut-off, we focus on a system dominated by contribution of a time-dependent torsion scalar induced by the spin of matter. In this regime, our results show that even very weak torsion causes cosmic acceleration. Specifically, we find that minima of the current equation of state for holographic dark energy, $(\omega_X^{0})_{min}$, lies in the range $-1 < (\omega_X^{0})_{min} < -0.778$ as a free parameter $d$ varies from $1$ to $0.654$. Focusing on the free parameter $d \approx 1$, we find that $(\omega_X^{0})_{min}$ exhibits slightly different behavior from the cosmological constant. Introducing torsion allows the Hubble radius to serve as a viable IR cut-off even without assuming the interaction between them. Moreover, this approach provides a non-interacting limit not found in earlier interacting models that use the Hubble radius as the IR cut-off.