Torsion is not some exotic bolt-on to general relativity. It is the part of the affine connection that Einstein’s theory sets to zero by hand. In Einstein–Cartan gravity, torsion is sourced by the intrinsic, quantum-mechanical spin of matter, and its effects normally become competitive only at the most extreme fermion densities imaginable. The theory has a celebrated pedigree: in the 1970s, physicists showed that torsion could avert the initial singularity, replacing the Big Bang with a cosmic bounce. But a recent proposal by researchers Yun and Lee went much further, claiming that in Einstein–Cartan cosmology the scalar torsion mode could rescue a famously broken model of dark energy, produce late-time acceleration, and even allow the equation of state to cross the so-called phantom divide, with possible relevance to the DESI anomaly. The new paper shows, with brutal clarity, that the claim fails, and that it fails for reasons reaching well beyond this particular model.

The technical heart of the argument is a single scaling relation. If the matter sector of the universe is separately conserved, the homogeneous torsion scalar Phi must obey a dilution equation that forces it to fall as the inverse cube of the scale factor. When this mode enters the Friedmann constraint, it appears as a negative energy density scaling as the inverse sixth power of the scale factor, a stiff component with an effective equation of state equal to plus one. This combination is an old acquaintance in disguise: it is precisely how the spin–spin contact interaction of a Weyssenhoff spin fluid enters Einstein–Cartan cosmology, where it powers the nonsingular bounce at high density. The physics under scrutiny is therefore the classical Einstein–Cartan bounce, examined at the opposite end of cosmic history, and the question is how much room the data leave for it there.

The first casualty is the holographic dark energy component itself. Holographic dark energy ties the dark energy density to an infrared cutoff length scale, and the most natural choice, the Hubble radius, famously fails in ordinary general relativity: because the density is proportional to the square of the Hubble rate, it merely tracks the dominant component and can never drive acceleration. That failure is why the field migrated to the future event horizon, with all its causality troubles. Yun and Lee claimed torsion changes this verdict. The new analysis shows it does not. Because the holographic density is proportional to H squared, it drops out of the deceleration parameter identically: the deceleration parameter is the same function of matter and torsion with or without it. Whatever acceleration the model produces belongs to torsion alone, and the cancellation is structural, not an accident of the quadratic choice. Any cutoff built from the Hubble rate alone inherits its dynamics from the other components instead of supplying its own, torsion or no torsion.

So where does the acceleration actually come from? From the bounce, and only from the bounce. The constraint that the Hubble rate squared must remain nonnegative enforces a turning point at which the expansion rate vanishes, the classical Einstein–Cartan bounce. The entire accelerating regime is confined to a transient window around that bounce, spanning less than a factor of about 1.6 in scale factor. The universe exits the bounce super-accelerating, crosses the phantom divide partway through the window, stops accelerating at its edge, and then settles into behaving like cold matter with a rapidly fading memory of the bounce. The window through which torsion could accelerate the universe closes before any observer can look through it. Dragging that window to redshifts where acceleration is actually observed would force the Hubble rate to vanish in our recent past, and the measured expansion history says emphatically otherwise.

What turns this qualitative observation into hard numbers is a requirement almost embarrassing in its modesty: the universe must contain its own past. Because the torsion term grows as the sixth power of one plus redshift going backward in time, faster than matter, radiation, or anything else, demanding that the expansion rate remain real up to some redshift the universe demonstrably reached yields a ladder of nested upper bounds on the torsion density parameter. A fit to the official DESI DR2 baryon acoustic oscillation likelihood gives a bound of 8.7 times ten to the minus four at 95 percent confidence. The mere existence of the spectroscopically confirmed galaxy JADES-GS-z14-0 at redshift 14.32 tightens this to 8.4 times ten to the minus five. The cosmic microwave background pushes it to 3.1 times ten to the minus ten. And Big Bang nucleosynthesis crushes it to 5 times ten to the minus twenty-four. Each rung rests on strictly weaker assumptions than the one before, and the last one settles the question beyond any reasonable doubt.

The DESI fit itself is a model of care. The authors used the released data vector and covariance exactly as distributed with the collaboration likelihood, thirteen entries spanning the brightest galaxy sample and six anisotropic tracers, and validated their pipeline by reproducing the published DESI Lambda-CDM fit to full precision before opening the torsion parameter. The result: the data express no preference whatsoever for torsion, with a negligible improvement in chi-squared. Even saturating the weakest bound would place the torsion-induced turning point at a redshift of roughly six, leaving no universe for the quasars and galaxies we observe beyond that epoch. The baryon acoustic data run out of constraining power exactly where the existence bounds take over, a striking convergence of independent lines of evidence.

The imprint on today’s dark energy equation of state makes the irrelevance concrete. The torsion contribution shifts the effective equation of state by an amount bounded by twice the torsion density parameter divided by the dark energy density. Even the weakest rung of the ladder caps this shift at a few parts in a thousand, on the phantom side of minus one, where DESI does not want it. The DESI preference for evolving dark energy asks for deviations of order a quarter on the quintessence side. That is a gap of two orders of magnitude at best, and twenty-two at worst, with the wrong sign throughout. In the Granda–Oliveros cutoff, an alternative infrared choice that includes the Hubble derivative, the verdict inverts in a darkly comic way: torsion does not prevent the big-rip singularity, it deepens it, adding to the super-acceleration instead of moderating it as it becomes ever more irrelevant on approach to the rip.

Every no-go theorem is a list of assumptions read backwards, and this one has a short list. The load-bearing assumption is adiabaticity: the requirement that matter be separately conserved, which forces the inverse-cube scaling. The authors show in an appendix that this scaling is nothing deeper than dilution, the kinematics of a comoving spin fluid whose particle number falls as the volume grows. Escaping the no-go therefore costs real physics. One must let matter and torsion exchange energy, turning the conservation identity into the definition of an interacting dark sector, and demand a spin density that refuses to dilute, through progressive spin alignment, condensation, or some other mechanism operating at late times. In Einstein–Cartan gravity torsion is algebraic and cannot outlive its source, so the mechanism must live in the matter sector explicitly, making a fermionic dark matter component with evolving spin alignment the natural candidate. Either sign of the spin contact term lands on the same verdict: no late-time acceleration from the adiabatic mode, with the sign merely deciding whether the early universe gets a bounce in compensation.

The authors are careful to delimit their target. Torsion cosmology at large survives this paper. Dynamical torsion in Poincaré gauge theory, where propagating modes can oscillate and drive late-time acceleration, remains untouched, as do interacting matter–torsion scenarios and the steady-state vectorial mode, which has already been confronted with DESI, supernova and microwave background data with results consistent with zero at sub-percent precision. But the message for the holographic dark energy program is stark. The Hubble cutoff’s Einstein–Cartan incarnation inherits, intact, the defect identified two decades ago: proportionality to the Hubble rate squared makes it a spectator. Torsion adds a bounce, and the bounce brings a brief phantom display, but every part of it stays locked behind a wall at high redshift. The window through which torsion could have accelerated the universe sits, and always sat, on the far side of that wall. If torsion has something to say about dark energy, it will have to say it where adiabaticity breaks, and that is precisely where the authors say their work is heading next.

Subject of Research: A no-go result for torsion-based holographic dark energy in Einstein–Cartan cosmology

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

Article References: Izaurieta, F., Lepe, S., & Quinzacara, C. (2026). No late-time role for adiabatic torsion: a no-go result for Hubble-cutoff holographic dark energy in Einstein–Cartan cosmology. The European Physical Journal C, 86(9), Article 1088. https://doi.org/10.1140/epjc/s10052-026-16337-0

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16337-0

Keywords: dark energy, torsion, Einstein–Cartan gravity, holographic dark energy, DESI, cosmology, no-go theorem, phantom divide, Big Bang nucleosynthesis, cosmic microwave background, baryon acoustic oscillations, Hubble radius