⚛️ general relativity

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

This paper demonstrates that adiabatic torsion in Einstein--Cartan cosmology cannot rescue the Hubble-cutoff holographic dark energy model to explain late-time acceleration or DESI anomalies, as it produces only a transient acceleration window and is strictly constrained by observational data to have a negligible impact on the dark energy equation of state.

Original authors: Fernando Izaurieta, Samuel Lepe, Cristian Quinzacara

Published 2026-07-21

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CC BY 4.0

Original authors: Fernando Izaurieta, Samuel Lepe, Cristian Quinzacara

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Mystery: Why the Universe is Speeding Up

Imagine the universe as a giant, expanding balloon. For decades, astronomers have been watching this balloon inflate, expecting it to slow down as gravity pulls everything back together, like a thrown ball losing speed as it rises. But in the late 1990s, a shocking discovery changed everything: the balloon isn't just inflating; it's inflating faster and faster. Something invisible is pushing the universe apart, a mysterious force scientists call "Dark Energy."

To understand this force, physicists often play a game of "cosmic detective." They look at the rules of the universe—specifically, how space and time are woven together. The standard rulebook is called General Relativity, which treats space as a smooth, stretchy fabric. But there's a secret chapter in the rulebook called Einstein–Cartan theory. In this version, space isn't just smooth; it can also have a tiny, microscopic "twist" or "kink" called torsion. Think of torsion like the twist in a rope or the spiral of a DNA strand. Usually, this twist is so small it doesn't matter, but some scientists wondered: could this twist be the secret engine driving the universe's acceleration?

Recently, a team of researchers proposed a specific idea: maybe this "twist" in space, combined with a clever way of measuring the universe's size (called the "Hubble cutoff"), could explain why we are speeding up. They suggested that this twist acts like a hidden battery, giving the universe a boost. But before we get too excited, a new paper by Fernando Izaurieta, Samuel Lepe, and Cristian Quinzacara has come along to check the math. They didn't just look at the idea; they put it under a microscope to see if it actually works with the real data we have from telescopes.

The Twist That Wasn't

The story of this paper is a bit like a detective story where the suspect turns out to be innocent, but for a very specific reason. The researchers were investigating a proposal that claimed the "twist" in space (torsion) could save a popular theory of Dark Energy. The theory in question, called Holographic Dark Energy, tries to explain the universe's acceleration by saying the energy density depends on the size of the universe's "horizon" (the furthest distance we can see). The problem was that this theory usually fails to explain acceleration unless you pick a very specific, tricky horizon. The new proposal said, "Wait! If we add the space-twist, the math works, and the Hubble horizon becomes a valid choice again!"

The authors of this paper, however, decided to run the numbers themselves. They started by looking at how this "twist" behaves. In their model, the twist is tied to the spin of particles (like tiny spinning tops). If the universe expands and the particles spread out, the twist gets weaker very quickly, fading away like a spinning top losing momentum. The paper shows that this fading twist acts like a "negative energy" that pushes the universe, but only for a very short, specific moment in cosmic history.

Here is the big reveal: The twist cannot explain the acceleration we see today.

The authors found that the "twist" only creates a burst of acceleration right after a "bounce" (a moment where the universe stops shrinking and starts expanding). This burst happens in a tiny window of time—so short that the universe only grows by a factor of about 1.6 during the entire acceleration phase. If you try to stretch this window to match the billions of years of acceleration we actually observe, you run into a massive problem. To make the math work for today, the universe would have to have stopped expanding and started shrinking again just a few billion years ago. But telescopes tell us the universe has been expanding smoothly and steadily ever since. The data simply doesn't allow for a universe that stopped and restarted recently.

The "No-Go" Ladder

To prove their point, the authors built a "ladder" of constraints, checking how much of this "twist" could possibly exist without breaking the known history of the universe. They used a parameter called $\Omega_\Phi$ to measure how strong the twist is today.

The First Rung (DESI Data): They looked at the latest measurements from the DESI (Dark Energy Spectroscopic Instrument) survey, which maps the positions of millions of galaxies. Even without assuming anything else, the data says the twist must be incredibly weak. They calculated that the twist's contribution must be less than $8.7 \times 10^{-4}$ (that's 0.00087) of the total energy budget.
The Second Rung (Ancient Galaxies): They then looked at the existence of a very old galaxy, JADES-GS-z14-0, which is so far away it existed when the universe was only about 300 million years old (at a redshift of $z = 14.32$ ). If the twist were any stronger, the universe would have collapsed before this galaxy could form. This pushes the limit down to $8.4 \times 10^{-5}$ .
The Third Rung (The Cosmic Microwave Background): Looking even further back to the "baby picture" of the universe (the CMB), the limit tightens to $3.1 \times 10^{-10}$ .
The Final Rung (Big Bang Nucleosynthesis): The strongest blow comes from the very first few minutes of the universe, when the first atoms were forming. If the twist were stronger than $5 \times 10^{-24}$ , it would have messed up the formation of these atoms, and we wouldn't be here.

The conclusion is stark: the twist is so weak today that it is practically invisible. It cannot be the engine driving the universe's current acceleration.

The Phantom Divide and the Wrong Side of the Wall

The original proposal hoped that this twist would not only explain acceleration but also allow the universe to cross a mysterious boundary called the "phantom divide" (where the dark energy gets so strong it could eventually rip the universe apart). The authors found that while the twist does allow for this crossing, it happens in that tiny, early window of the "bounce" we mentioned earlier. By the time we get to the present day, the twist has faded so much that it can't do anything.

In fact, the paper shows that if you try to force this twist to explain today's acceleration, you end up predicting a "phantom" behavior that is on the wrong side of the line. The DESI data suggests the universe is behaving like "quintessence" (a gentle, evolving force), but the twist model predicts a "phantom" behavior (a violent, ripping force) that is two to twenty-two orders of magnitude too weak to matter, and on the wrong side of the equation entirely.

What About Other Twists?

Does this mean all ideas about space-twists are dead? Not quite. The authors are careful to say they only ruled out the "adiabatic" twist—the kind that fades away naturally as particles spread out. They suggest that if the twist interacts with matter in a more complex way (like if the particles' spins align or change over time), it might still have a chance. But the simple, "fading" version that was proposed to save the Hubble cutoff is definitely out.

They also checked a different version of the theory called the "Granda–Oliveros" cutoff. Instead of fixing the problem, they found that the twist actually makes the "Big Rip" (the scenario where the universe tears itself apart) happen sooner and more violently.

The Verdict

In the end, this paper is a reality check. It shows that while the idea of a "twisted" universe is mathematically fascinating and has a cool history, the specific version that was supposed to rescue the Hubble cutoff for Dark Energy doesn't hold up against the evidence. The twist is a relic of the very early universe, a remnant of a "bounce" that happened long ago. It fades away too fast to be the mysterious force pushing our universe apart today.

The authors conclude that if torsion is going to explain Dark Energy, it will have to break the rules of "adiabaticity" (the rule that says it just fades away). It would need to find a way to stay strong or interact with matter in a new, unexpected way. Until then, the "twist" remains a ghost from the past, not the driver of our future.

Technical Summary: No Late-Time Role for Adiabatic Torsion in Einstein–Cartan Cosmology

Problem Statement
Recent claims by Yun and Lee [11, 12] suggested that the homogeneous scalar torsion mode ( $\Phi$ ) in Einstein–Cartan (EC) gravity could rescue the Hubble radius ( $L=H^{-1}$ ) as a viable infrared cutoff for Holographic Dark Energy (HDE). Specifically, they proposed that this torsion mode could induce late-time cosmic acceleration and allow the effective equation of state to cross the phantom divide ( $\omega < -1$ ), potentially explaining the evolving dark energy preference observed in DESI DR2 data. This paper investigates whether the adiabatic torsion mode, which scales as $\Phi \propto a^{-3}$ , can indeed support such a late-time role without violating established cosmological constraints.

Methodology and Theoretical Framework
The authors analyze the Friedmann equations derived from EC gravity with a homogeneous scalar torsion mode $\Phi(t)$ in a flat FLRW metric. The system is governed by:

$3H^2 = \rho - 3\Phi^2$
$\dot{H} + H^2 = -\frac{1}{6}(\rho + 3p - 12\Phi^2)$

The study focuses on the "adiabatic" case where the matter sector is separately conserved ( $\dot{\rho} + 3H(\rho+p)=0$ ). Under this condition, the torsion scalar obeys $\dot{\Phi} + 3H\Phi = 0$ , leading to the scaling $\Phi \propto a^{-3}$ . Consequently, the torsion contribution acts as a stiff fluid with negative energy density ( $\rho_\Phi = -3\Phi^2 \propto -a^{-6}$ and $p_\Phi = \rho_\Phi$ ).

The authors derive the deceleration parameter $q$ and the effective equation of state $\omega_{\text{eff}}$ for models incorporating both HDE (with Hubble or Granda–Oliveros cutoffs) and this torsion mode. They then confront the model with observational data by:

Analyzing the kinematic constraints imposed by the condition $H^2 \geq 0$ (the existence of a classical bounce).
Fitting the model to the DESI DR2 Baryon Acoustic Oscillation (BAO) likelihood using a Markov Chain Monte Carlo (MCMC) approach.
Deriving upper bounds on the torsion density parameter $\Omega_\Phi \equiv (\Phi_0/H_0)^2$ based on the existence of high-redshift objects (JADES-GS-z14-0 at $z=14.32$ , CMB at $z \approx 1090$ , and Big Bang Nucleosynthesis at $z \approx 4.3 \times 10^9$ ).

Key Findings and Results

Dynamical Inertness of HDE: The authors demonstrate that when the Hubble cutoff is used ( $\rho_{\text{hol}} \propto H^2$ ), the holographic density term drops out of the expression for the deceleration parameter $q$ . The acceleration is driven entirely by the torsion term, not the holographic component. The holographic density merely renormalizes the Friedmann constraint but does not alter the dynamics of acceleration.
The Transient Acceleration Window: The model produces acceleration only in a narrow window immediately following the EC bounce, defined by $\bar{a} \leq a < 4^{1/3}\bar{a}$ (where $H(\bar{a})=0$ ). This window spans a scale factor range of less than a factor of 1.6.
- To place this acceleration window at observable late-time redshifts (e.g., $z \sim 0.5$ ), the bounce must have occurred very recently.
- This forces the Hubble rate $H$ to vanish in the recent past, contradicting the measured expansion history which shows continuous expansion.
Nested Upper Bounds on $\Omega_\Phi$ : The requirement that the universe contains its own past (i.e., $H^2(z) > 0$ for all observed redshifts) imposes strict upper limits on the present-day torsion density $\Omega_\Phi$ :
- DESI DR2 BAO fit: $\Omega_\Phi < 8.7 \times 10^{-4}$ (95% CL).
- Existence of JADES-GS-z14-0 ( $z=14.32$ ): $\Omega_\Phi < 8.4 \times 10^{-5}$ .
- CMB ( $z \approx 1090$ ): $\Omega_\Phi < 3.1 \times 10^{-10}$ .
- Big Bang Nucleosynthesis (BBN): $\Omega_\Phi < 5 \times 10^{-24}$ .
Impact on Dark Energy Equation of State: The shift in the dark energy equation of state today is bounded by $|1 + \omega_0| \leq 2\Omega_\Phi/\Omega_\Lambda$ . Even using the weakest bound (DESI fit), the deviation is $|1 + \omega_0| \lesssim 2.5 \times 10^{-3}$ , which is two orders of magnitude smaller than the $\sim 0.25$ preference for evolving dark energy seen in DESI data. Furthermore, the model predicts a phantom-side crossing ( $\omega < -1$ ), whereas DESI prefers a quintessence-like evolution ( $\omega > -1$ ).
Granda–Oliveros Cutoff: In the case of the Granda–Oliveros cutoff ( $\rho_{\text{hol}} \propto \alpha H^2 + \beta \dot{H}$ ), the torsion term does not prevent the Big Rip singularity; instead, it deepens the super-acceleration ( $q < -1$ ), hastening the singularity.

Significance and Conclusions
The paper concludes that the claim by Yun and Lee fails: the adiabatic torsion mode $\Phi \propto a^{-3}$ cannot rescue the Hubble cutoff as a viable late-time dark energy mechanism. The acceleration and phantom crossing observed in the model are artifacts of the transient EC bounce, confined to a regime that is observationally excluded by the existence of high-redshift structures and the CMB.

The authors emphasize that this "no-go" result is specific to the adiabatic assumption (separate conservation of matter and torsion). The scaling $\Phi \propto a^{-3}$ is identified as the kinematic consequence of a diluting spin fluid. To evade this result, one would need to break adiabaticity, allowing energy exchange between matter and torsion (e.g., via evolving spin alignment in a dark matter sector) to sustain a slower decay of torsion. However, within the standard adiabatic framework, torsion is relegated to early-universe physics (the bounce) and is cosmologically irrelevant at late times.

The paper asserts that while this specific adiabatic mode is ruled out, dynamical torsion models (e.g., propagating modes in Poincaré gauge theory) or non-adiabatic scenarios remain open avenues for investigation, though they require distinct physical mechanisms beyond simple dilution.