No late-time role for adiabatic torsion: a no-go result for Hubble-cutoff holographic dark energy in Einstein--Cartan cosmology

Abstract

In Friedmann cosmology with Einstein--Cartan torsion, the homogeneous torsion mode compatible with a separately conserved matter sector scales as $\Phi\propto a^{-3}$ and enters the Friedmann constraint as a stiff component of negative energy density, $-3\Phi^{2}\propto a^{-6}$. It has recently been claimed that this mode rescues the Hubble radius as an infrared cutoff for holographic dark energy, producing late-time acceleration and a phantom-divide crossing of possible relevance to DESI. We show that it cannot. With the Hubble cutoff the holographic density drops out of the deceleration parameter, and the only accelerating regime is the transient window $\bar{a}\leq a<4^{1/3}\bar{a}$ around the torsion bounce at $H(\bar{a})=0$; placing that window at observable redshifts would force the Hubble rate to vanish in our recent past, against the measured expansion history. Requiring a viable history yields nested upper bounds on $\Omega_{\Phi}\equiv(\Phi_{0}/H_{0})^{2}$: fitting the official DESI DR2 BAO likelihood gives $\Omega_{\Phi}<8.7\times10^{-4}$ ($95\%$ CL), the existence of a spectroscopically confirmed galaxy at $z=14.32$ gives $8.4\times10^{-5}$, the CMB gives $3.1\times10^{-10}$, and Big Bang nucleosynthesis gives $5\times10^{-24}$. Today's imprint on the dark energy equation of state, $|1+\omega_{0}|\leq2\Omega_{\Phi}/\Omega_{\Lambda}$, falls short of the DESI preference by two orders of magnitude at best and twenty-two at worst, and on the phantom side. In the Granda--Oliveros cutoff, torsion deepens rather than prevents the big-rip singularity. An appendix derives the Friedmann pair from the Einstein--Cartan field equations and shows that the $a^{-3}$ scaling is the kinematics of a diluting spin fluid; escaping the no-go requires breaking exactly that.