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Abstract The cluster mass–richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the matter density Ω_mand the amplitude of fluctuationsσ₈using the cluster abundance technique. We derive the MRR relation usingGalWCat19, a publicly available galaxy cluster catalog we created from the Sloan Digital Sky Survey-DR13 spectroscopic data set. In the MRR, cluster mass scales with richness as $\log M_{200}=\alpha +\beta \log N_{200}$. We find that the MRR we derive is consistent with both the IllustrisTNG and mini-Uchuu cosmological numerical simulations, with a slope ofβ≈ 1. We use the MRR we derived to estimate cluster masses from theGalWCat19catalog, which we then use to set constraints on Ω_mandσ₈. Utilizing the all-member MRR, we obtain constraints of Ω_m= ${0.31}_{-0.03}^{+0.04}$andσ₈= ${0.82}_{-0.04}^{+0.05}$, and utilizing the red member MRR only, we obtain Ω_m= ${0.31}_{-0.03}^{+0.04}$andσ₈= ${0.81}_{-0.04}^{+0.05}$. Our constraints on Ω_mandσ₈are consistent and very competitive with the Planck 2018 results. 

ABSTRACT We measure the two-point correlation function (CF) of 1357 galaxy clusters with a mass of log10M200 ≥ 13.6 h−1 M⊙ and at a redshift of z ≤ 0.125. This work differs from previous analyses in that it utilizes a spectroscopic cluster catalogue, $$\tt {SDSS-GalWCat}$$, to measure the CF and detect the baryon acoustic oscillation (BAO) signal. Unlike previous studies which use statistical techniques, we compute covariance errors directly by generating a set of 1086 galaxy cluster light-cones from the GLAM N-body simulation. Fitting the CF with a power-law model of the form ξ(s) = (s/s0)−γ, we determine the best-fitting correlation length and power-law index at three mass thresholds. We find that the correlation length increases with increasing the mass threshold while the power-law index is almost constant. For log10M200 ≥ 13.6 h−1 M⊙, we find s0 = 14.54 ± 0.87 h−1 Mpc and γ = 1.97 ± 0.11. We detect the BAO signal at s = 100 h−1 Mpc with a significance of 1.60σ. Fitting the CF with a Lambda cold dark matter model, we find $$D_\mathrm{V}(z = 0.089)\mathit{r}^{\mathrm{ fid}}_\mathrm{ d}/\mathit{r}_\mathrm{ d} = 267.62 \pm 26$$ h−1 Mpc, consistent with Planck 2015 cosmology. We present a set of 108 high-fidelity simulated galaxy cluster light-cones from the high-resolution Uchuu N-body simulation, employed for methodological validation. We find DV(z = 0.089)/rd = 2.666 ± 0.129, indicating that our method does not introduce any bias in the parameter estimation for this small sample of galaxy clusters. 

ABSTRACT Cold Dark Matter with cosmological constant (ΛCDM) cosmological models with early dark energy (EDE) have been proposed to resolve tensions between the Hubble constant $$H_0=100\, h$$ km ṡ−1Ṁpc−1 measured locally, giving h ≈ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early-Universe measurements plus ΛCDM, giving h ≈ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10 per cent of the cosmological energy density at the end of the radiation-dominated era at redshift z ∼ 3500. Here, we compare linear and non-linear predictions of a Planck-normalized ΛCDM model including EDE giving h = 0.728 with those of standard Planck-normalized ΛCDM with h = 0.678. We find that non-linear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1–2 per cent. However, the differences dramatically increase at high redshifts. The EDE model predicts 50 per cent more massive clusters at z = 1 and twice more galaxy-mass haloes at z = 4. Even greater increases in abundances of galaxy-mass haloes at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by the James Webb Space Telescope (JWST) observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2 per cent between the models – an effect that is not washed out by non-linearities. Both standard ΛCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but the Dark Energy Spectroscopic Instrument and Euclid measurements will provide stringent new tests.