REVIEW
The SRG/eROSITA All-Sky Survey: Early dark energy and Hubble constant from the cluster mass function
Cosmology and Nongalactic Astrophysics · Submitted 7 Sep 2026 · Published version · 300 references
Pith's verdict: First EDE constraints from cluster counts, but the 3.2-sigma detection is fragile — the halo mass function for EDE cosmologies is validated on only one simulation, and uncalibrated systematics could dissolve the signal.
T0 · AI review
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Referee report
The paper
The paper claims
Galaxy cluster counts from eROSITA yield a 3.2σ hint of early dark energy and a Hubble constant consistent with late universe measurements.
The reading
What carries the argument
The key machinery is the halo mass function for EDE cosmologies, constructed by computing the linear matter power spectrum with the EarlyQuintessence module in CAMB and adopting the Tinker et al. (2008) multiplicity function f(σ) calibrated in ΛCDM, under the assumtion that EDE affects clustering only through the linear power spectrum. The EDE model is parameterized by f_EDE (peak energy fraction), log10 z_c (critical redshift), and θ_i (initial field displacement). The cluster abundnce likelihood is compined with external CMB, lensing and BAO posteriors via kemel density estimtion.
Extended reading notes
Core claim
The paper estabishes that the cluster mass function, measured from 4196 eRASS1 clusters at z<0.45 with weak lemsing mass calibrtion, can constrain EDE paramters. While eRASS1 alone gives only an upper limit f_EDE<0.3, a full Bayesian joint analysis with external CMB, lensing and BAO datasets yields f_EDE = 0.$10^{{+0.04}}$_{-0.03}, log10(z_c)=3.53±0.09, and H₀=71.4±1.4 km $s^{{-1}}$ $Mpc^{{-1}}$. This result is obtained without any distnce-lawer calibration, making it an independent test that favors an EDE soltion to the Hubble tension.
Load-bearing premise
The analysis assumes that the Tinker et al. (2008) halo mass function calibration from ΛCDM simulations accurately describes cluster abundances in EDE cosmologies; this was validated against only one N-body simulation (Klypin et al. 2021) with fixed EDE paramters, and the paper notes no broader validation exists.
Editorial extensions
If this is right
- If the dection holds, the Hubble tenson between early and late universe measurements is reslved by an early dark energy component making up ~10 % of the energy density around recombinaton.
- The consisency between cluster counts and CMB+BAO data suges that large-scale structure and CMB jointy favor enhnced small-scale power, with implications for galxy formation at high redshift.
- Cluster abundance analyses become a new, independent probe of EDE, complementay to CMB primary anisotrpy and galxy clustering (e.g., BOSS full-shape).
- Future survys like eRASS2 will improve statistial precision by a factor of several, enabling a deisive test of the EDE hypothesis.
Original abstract
The evolution of the mass function of massive galaxy clusters is a well-established probe of cosmology. Using the eROSITA X-ray instrument on board the Spectrum Roentgen Gamma (SRG) mission, the western Galactic hemisphere of eROSITA's first All-Sky Survey (eRASS1) delivers a uniformly selected and securely confirmed sample of 5259 galaxy clusters spanning $0.1 < z < 0.8$. When combined with overlapping weak lensing data from DES Year 3, KiDS, and HSC for mass calibration, this dataset enables precise tests of the standard $\Lambda$CDM framework and beyond. In this work, we use the $0.1 < z < 0.45$ subsample of the eRASS1 cluster catalog to place constraints on an axion-like Early Dark Energy (EDE) scenario. Such models have been proposed as a possible mechanism to alleviate the tension between early- and late-Universe measurements of the Hubble constant. In this framework, a scalar field temporarily enhances the cosmic expansion rate around the epoch of recombination before rapidly diluting at later times, leaving distinct imprints on structure growth. We leverage these signatures to present the first constraints on EDE derived from galaxy cluster number counts. Using eRASS1 number counts alone, we obtain an upper limit on the maximum EDE fraction of $f_{\rm EDE} < 0.3$, consistent with primary CMB analyses. Combining our cluster analysis with primary CMB measurements, baryon acoustic oscillations, and CMB lensing, while notably excluding distance-ladder calibration data, yields results consistent with a nonzero EDE contribution and $H_0$ values compatible with late-Universe measurements. The most significant detection, at $\sim 3.2\sigma$, arises from the joint analysis of the eRASS1 sample with the full set of external datasets, yielding $f_{\rm EDE} = 0.10^{+0.04}_{-0.03}$ and $H_0 = 71.4 \pm 1.4$ km/s/Mpc. [ABRIDGED]
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The evolution of the mass function of massive galaxy clusters is a well-established probe of cosmology. Using the eROSITA X-ray instrument on board the Spectrum Roentgen Gamma (SRG) mission, the western Galactic hemisphere of eROSITA's first All-Sky Survey (eRASS1) delivers a uniformly selected and securely confirmed sample of 5259 galaxy clusters spanning $0.1 < z < 0.8$. When combined with overlapping weak lensing data from DES Year 3, KiDS, and HSC for mass calibration, this dataset enables precise tests of the standard $\Lambda$CDM framework and beyond. In this work, we use the $0.1 < z < 0.45$ subsample of the eRASS1 cluster catalog to place constraints on an axion-like Early Dark Energy (EDE) scenario. Such models have been proposed as a possible mechanism to alleviate the tension between early- and late-Universe measurements of the Hubble constant. In this framework, a scalar field temporarily enhances the cosmic expansion rate around the epoch of recombination before rapidly diluting at later times, leaving distinct imprints on structure growth. We leverage these signatures to present the first constraints on EDE derived from galaxy cluster number counts. Using eRASS1 number counts alone, we obtain an upper limit on the maximum EDE fraction of $f_{\rm EDE} < 0.3$, consistent with primary CMB analyses. Combining our cluster analysis with primary CMB measurements, baryon acoustic oscillations, and CMB lensing, while notably excluding distance-ladder calibration data, yields results consistent with a nonzero EDE contribution and $H_0$ values compatible with late-Universe measurements. The most significant detection, at $\sim 3.2\sigma$, arises from the joint analysis of the eRASS1 sample with the full set of external datasets, yielding $f_{\rm EDE} = 0.10^{+0.04}_{-0.03}$ and $H_0 = 71.4 \pm 1.4$ km/s/Mpc. [ABRIDGED]
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The evolution of the mass function of massive galaxy clusters is a well-established probe of cosmology. | background 1.00 | 0.03 | 0.01 | asserted 1.00 |
| s1 | Using the eROSITA X-ray instrument on board the Spectrum Roentgen Gamma (SRG) mission, the western Galactic hemisphere of eROSITA's first All-Sky Survey (eRASS1) delivers a uniformly selected and securely confirmed sample of 5259 galaxy clusters spanning $0.1 < z < 0.8$. | method 0.92 | 0.89 | 0.02 | asserted 1.00 |
| s2 | When combined with overlapping weak lensing data from DES Year 3, KiDS, and HSC for mass calibration, this dataset enables precise tests of the standard $\Lambda$CDM framework and beyond. | method 0.88 | 0.53 | 0.03 | asserted 0.94 |
| s3 | In this work, we use the $0.1 < z < 0.45$ subsample of the eRASS1 cluster catalog to place constraints on an axion-like Early Dark Energy (EDE) scenario. | contribution 0.67 | 0.96 | 0.05 | asserted 0.99 |
| s4 | Such models have been proposed as a possible mechanism to alleviate the tension between early- and late-Universe measurements of the Hubble constant. | background 1.00 | 0.04 | 0.02 | hedged possibility 0.92 |
| s5 | In this framework, a scalar field temporarily enhances the cosmic expansion rate around the epoch of recombination before rapidly diluting at later times, leaving distinct imprints on structure growth. | background 0.99 | 0.05 | 0.03 | asserted 0.99 |
| s6 | We leverage these signatures to present the first constraints on EDE derived from galaxy cluster number counts. | contribution 0.99 | 0.95 | 0.13 | asserted 1.00 |
| s7 | Using eRASS1 number counts alone, we obtain an upper limit on the maximum EDE fraction of $f_{\rm EDE} < 0.3$, consistent with primary CMB analyses. | result 1.00 | 0.97 | 0.13 | asserted 0.99 |
| s8 | Combining our cluster analysis with primary CMB measurements, baryon acoustic oscillations, and CMB lensing, while notably excluding distance-ladder calibration data, yields results consistent with a nonzero EDE contribution and $H_0$ values compatible with late-Universe measurements. | result 0.94 | 0.93 | 0.27 | hedged possibility 0.81 |
| s9 | The most significant detection, at $\sim 3.2\sigma$, arises from the joint analysis of the eRASS1 sample with the full set of external datasets, yielding $f_{\rm EDE} = 0.10^{+0.04}_{-0.03}$ and $H_0 = 71.4 \pm 1.4$ km/s/Mpc. [ABRIDGED] | result 1.00 | 0.96 | 0.80 | asserted 0.99 |
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Figures
Showing 6 of the paper's 8 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2609.07834 by the authors.
References
Discussion
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