Holographic dark energy with torsion

We consider the holographic dark energy model with axial torsion which satisfies the cosmological principle. Subsequently, by using the torsional analogs of Friedmann equations for the new equation from Einstein–Cartan gravity theory, we obtain the equation of state for dark energy in this model. We find that the extended holographic dark energy from the particle horizon as the infrared (IR) cut-off does not give the accelerating expansion of the universe. Also, employing the future event horizon as IR cut-off still achieves the accelerating expansion of the universe. In contrast, there is a possibility that the Hubble radius as IR cut-off achieves the accelerating expansion of the universe in superluminal region for axial torsion. More precisely, the current value of ratio for torsion to the matter density, \(\gamma ^{0}=0.5\) ${\gamma }^0=0.5$ gives the equation of state of dark energy \(\omega _{\Lambda }\cong -1\) ${\omega }_{\mathrm{\Lambda }}\cong -1$ .