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Ultra-light axion constraints from Planck and ACT: the role of nonlinear modelling

This study demonstrates that constraints on ultralight axion dark matter derived from Planck and ACT CMB data are highly sensitive to nonlinear modeling choices, revealing that naive prescriptions can artificially favor a subdominant axion component around $10^{-24}$ eV due to lensing-like enhancements in the CMB power spectrum.

Original authors: Lauren Gaughan, Anne M. Green, Adam Moss

Published 2026-05-13

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CC BY 4.0

Original authors: Lauren Gaughan, Anne M. Green, Adam Moss

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

Imagine the universe is a giant, invisible ocean made mostly of "dark matter." For a long time, scientists thought this ocean was made of heavy, slow-moving particles (like cold, sluggish fish). But there's a new theory suggesting some of this dark matter might be made of Ultralight Axions (ULAs). Think of these axions not as fish, but as ghostly, vibrating waves that ripple through the cosmos.

The paper you're asking about is a detective story. The authors are trying to figure out how much of this "ghostly wave" dark matter exists in our universe by looking at the Cosmic Microwave Background (CMB). You can think of the CMB as the "baby photo" of the universe, a faint glow of light left over from the Big Bang.

Here is the simple breakdown of their investigation:

1. The Problem: The "Blurry" Photo

When we look at the CMB, the light has traveled billions of years to reach us. On its way, it gets bent and distorted by the gravity of the dark matter it passes through. This is called gravitational lensing. It's like looking at a streetlight through a wavy glass window; the light gets smeared.

To understand the smearing, scientists need to know exactly how the dark matter is clumped together.

Cold Dark Matter clumps up easily, like sand piling into a mound.
Axions are wavy. Because they are so light, they have a "quantum pressure" that stops them from clumping too tightly on small scales. They are more like a mist that refuses to condense into a solid pile.

2. The Trap: The "Naive" Calculator

To predict how the universe looks today, scientists use computer models. The paper argues that many previous studies used a "naive" calculator.

The Analogy: Imagine you are trying to predict how a crowd of people will move in a stadium.

The Naive Model assumes everyone is a solid, heavy person who can push through walls and pile up anywhere.
The Reality is that some people in the crowd are actually made of mist (the axions). They can't pile up; they just flow around.

When the scientists used the "naive" model (which assumes everything is solid), it accidentally created a fake signal. It made the universe look like it had more clumping than it actually did. This fake clumping looked suspiciously like the signal we would expect if there were a specific amount of axion dark matter (specifically, axions with a mass around $10^{-24}$ eV).

3. The Discovery: It Was a Glitch, Not a Ghost

The authors, Lauren Gaughan, Anne Green, and Adam Moss, decided to fix the calculator. They used a new, more sophisticated model called axionHMcode.

The Analogy: They swapped the "solid person" calculator for a "mist-aware" calculator. They told the computer: "Hey, remember, the axions are waves, not solid rocks. They can't clump in the same way."

The Result:

When they used the naive model, the data seemed to say: "Yes! We found axions! There is about 17% of them!" (This was a false alarm).
When they used the correct "mist-aware" model, that excitement vanished. The data no longer showed a strong preference for axions. The "ghost" was just a glitch in the math.

4. Why This Matters

The paper focuses on a specific range of axion masses (between $10^{-25}$ and $10^{-23}$ eV). In this range, the "wavy" nature of the axions interacts with the universe in a way that is very sensitive to how we do the math.

The authors found that:

The math matters more than we thought: If you use the wrong way to model how these particles clump, you can trick yourself into thinking you found new physics when you haven't.
The "Fake" Signal: The naive model created an artificial "boost" in the data that looked like extra lensing. This made the universe look like it had more axions than it actually does.
The Conclusion: When they did the math correctly, the evidence for these specific axions became much weaker. The "preference" for axions dropped from a "maybe" to a "probably not."

Summary

Think of this paper as a warning label on a scientific instrument. The authors are saying: "Be careful how you measure the universe. If you use a ruler designed for solid objects to measure a cloud, you might think the cloud is heavier than it really is."

They showed that previous claims of finding a specific type of dark matter might have been an illusion caused by using a simplified math model. By using a more accurate model that respects the "wavy" nature of axions, the evidence for their existence in this specific mass range has significantly weakened.

Technical Summary: Ultra-light axion constraints from Planck and ACT: the role of nonlinear modelling

Problem Statement
This study investigates the dependence of constraints on the abundance of ultralight axions (ULAs) on the choice of nonlinear modelling in cosmological analyses. The authors focus on the axion mass range $10^{-25} \le m/\text{eV} \le 10^{-23}$ . In this regime, the axion Jeans scale falls within the quasi-linear regime ( $k \sim 0.1\text{--}1 \, h \, \text{Mpc}^{-1}$ ) probed by Cosmic Microwave Background (CMB) lensing. While standard analyses often rely on linear theory or standard nonlinear prescriptions calibrated for Cold Dark Matter (CDM), the authors argue that these approaches may be insufficient for Mixed Dark Matter (MDM) cosmologies containing ULAs. Specifically, they aim to determine whether naive nonlinear modelling introduces artificial preferences for a subdominant ULA component, thereby biasing constraints on the axion fraction ( $f_{\text{ax}}$ ).

Methodology
The authors perform Markov Chain Monte Carlo (MCMC) analyses using the Boltzmann solver AxiCAMB, which incorporates the improved Passaglia and Hu (PH) Effective Fluid Approximation (EFA) to handle axion oscillations. They utilize data from:

Planck 2018: Low- $\ell$ temperature (TT) and SRoll2 polarization (EE) likelihoods.
ACT DR6: Foreground-marginalized CMB-only TT/TE/EE likelihoods and CMB lensing potential power spectrum ( $C_L^{\phi\phi}$ ).
DESI DR2: Baryon Acoustic Oscillation (BAO) measurements.

The study compares three distinct nonlinear modelling prescriptions within the context of MDM cosmologies:

Naive HMcode: A standard application of HMcode-2020 (calibrated for CDM) to the total matter power spectrum, treating the ULA component as if it were a standard cold component despite its wave-like suppression.
axionHMcode (Basic): A halo model calibrated against ULA simulations, summing one-halo and two-halo terms without additional smoothing ( $\alpha=1$ ).
axionHMcode (DOME): A refined halo model with improved concentration-mass relations and independent smoothing parameters for cold–cold and cold–axion spectra, calibrated to mixed-dark-matter simulations.

The analysis is conducted at fixed axion masses ( $m = 10^{-25}, 10^{-24}, 10^{-23}$ eV) using two data combinations: primary CMB spectra only (P-ACT) and primary CMB plus lensing and BAO data (P-ACT-LB).

Key Contributions and Results

Artificial Preference for ULAs: The authors find that the "naive" nonlinear modelling of non-cold matter produces a significant, artificial preference for a subdominant ULA component with mass $m \approx 10^{-24}$ eV. Using the naive model with P-ACT data, the axion model shows an apparent improvement over $\Lambda$ CDM of $\Delta\chi^2 \approx -4.56$ (nominal $\sim 2.1\sigma$ ).
Mechanism of Bias: This spurious preference arises because the naive model incorrectly shifts internal HMcode parameters (specifically the effective spectral index $n_{\text{eff}}$ and smoothing parameter $\alpha$ ) when applied to a power spectrum with axion-induced suppression. This leads to an overestimation of the nonlinear boost in the quasi-linear regime ( $k \sim 0.3\text{--}1 \, h \, \text{Mpc}^{-1}$ ) at redshifts $z \sim 2$ (where CMB lensing peaks). The resulting enhancement mimics the effect of enhanced lensing (similar to the Planck preference for $A_{\text{lens}} > 1$ ), allowing the axion model to fit the data better than $\Lambda$ CDM in the naive scenario.
Sensitivity to Nonlinear Prescription: When using the more physically motivated axionHMcode (Basic or DOME) prescriptions, the apparent preference for axions is substantially reduced. For $m = 10^{-24}$ eV, the $\Delta\chi^2$ improvement drops to $\sim -1.99$ (Basic) and $\sim -3.14$ (DOME) with P-ACT data.
Impact of Lensing Data: The inclusion of direct CMB lensing measurements (P-ACT-LB) highlights the sensitivity of constraints to nonlinear modelling. The lensing potential power spectrum ( $C_L^{\phi\phi}$ ) shows differences of 5–15% between the naive and axionHMcode models at $L \gtrsim 500$ , whereas primary CMB spectra show sub-percent differences. Consequently, the constraints on $f_{\text{ax}}$ tighten significantly when lensing data is included and accurate nonlinear modelling is used.
Constraints on $f_{\text{ax}}$ : With the P-ACT-LB combination and the Basic axionHMcode model, the 95% upper limits on the axion fraction are tightened compared to the naive model. For $m = 10^{-24}$ eV, the limit is $f_{\text{ax}} < 0.032$ (Basic) versus a looser constraint or preference for non-zero $f_{\text{ax}}$ in the naive case.

Significance and Claims
The paper concludes that nonlinear modelling is a leading systematic uncertainty in CMB-lensing constraints on ultralight axions in the mass range $10^{-25} \le m/\text{eV} \le 10^{-23}$ . The authors claim that the apparent statistical preference for axions found in previous analyses using naive nonlinear prescriptions is likely an artefact of the modelling rather than evidence for new physics. They emphasize that:

The inferred constraints depend significantly on the choice of nonlinear model.
Naive CDM-calibrated prescriptions can generate a "lensing-like" enhancement in the CMB power spectrum, mimicking an axion signal.
Accurate modelling of mixed-dark-matter halos (via axionHMcode) is essential to avoid spurious detections.
Future high-precision CMB lensing measurements (e.g., from the Simons Observatory) will be strongly affected by these systematics, necessitating further validation of nonlinear prescriptions against simulations spanning relevant axion masses and fractions.

The authors do not claim a detection of ULAs; rather, they demonstrate that current constraints are highly model-dependent and that previous "improvements" in fit quality may be illusory.

1. The Problem: The "Blurry" Photo

2. The Trap: The "Naive" Calculator

3. The Discovery: It Was a Glitch, Not a Ghost

4. Why This Matters

Summary

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