The SRG/eROSITA All-Sky Survey: Early dark energy and Hubble constant from the cluster mass function

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]