Built-in precision: Improving cluster cosmology through the self-calibration of a galaxy cluster sample

TL;DR

This work forecasts how incorporating the clustering power spectrum of galaxy clusters, alongside abundance measurements from future tSZ surveys, improves constraints on $w$ and $Ω_M$ using self-calibration. Leveraging the HalfDome simulations, redshift uncertainties, and a tSZ mass–observable scaling relation, the authors quantify gains across cluster samples of 33k–140k and under varying priors on the scaling relation, finding that clustering mainly tightens $Ω_M$ and $w$, while also constraining $B_{sz}$ and $C_{sz}$. The improvements scale with sample size and weaken external priors, offering an internal cross-check on the mass-observable evolution without extra data. By demonstrating substantial, context-sensitive gains, the study supports adopting clustering-based self-calibration in upcoming cluster cosmology programs to maximize science return.

Abstract

We examine the potential improvements in constraints on the dark energy equation of state parameter $w$ and matter density $Ω_M$ from using clustering information along with number counts for future samples of thermal Sunyaev-Zel'dovich selected galaxy clusters. We quantify the relative improvement from including the clustering power spectrum information for three cluster sample sizes from 33,000 to 140,000 clusters and for three assumed priors on the mass slope and redshift evolution of the mass-observable relation. As expected, clustering information has the largest impact when (i) there are more clusters and (ii) the mass-observable priors are weaker. For current knowledge of the cluster mass-observable relationship, we find the addition of clustering information reduces the uncertainty on the dark energy equation of state, $σ(w)$, by factors of $1.023\pm 0.007$ to $1.0790\pm 0.011$, with larger improvements observed with more clusters. Clustering information is more important for the matter density, with $σ(Ω_M)$ reduced by factors of $1.068 \pm 007$ to $1.145 \pm 0.012$. The improvement in $w$ constraints from adding clustering information largely vanishes after tightening priors on the mass-observable relationship by a factor of two. For weaker priors, we find clustering information improves the determination of the cluster mass slope and redshift evolution by factors of $1.389 \pm 0.041$ and $1.340 \pm 0.039$ respectively. These findings highlight that, with the anticipated surge in cluster detections from next generation surveys, self-calibration through clustering information will provide an independent cross-check on the mass slope and redshift evolution of the mass-observable relationship as well as enhancing the precision achievable from cluster cosmology.

Figures (3)

• Figure 1: Measured bandpowers compared to theoretical predictions across three redshift bins for one realisation of the 33k cluster sample. The impact of clustering is most significant at low angular multipoles ($\ell < 300$), and drops towards zero at higher multipoles. The amplitude in the power spectrum increases at lower redshifts due to the continued growth of structure over time.
• Figure 2: The convergence of the covariance matrix estimate as $N_{BS}$ is increased. The covariance is well-estimated with $N_{BS}= 5000$ samples, with $<5\%$ shifts when doubling the number of draws to $N_{BS}= 10000$.
• Figure 3: 1- and 2-$\sigma$ contours for a simulated 140k cluster sample with pessimistic scaling relation priors. The posteriors with from the cluster abundance measurement are shown in blue, while the posteriors with the measurement of the clustering power spectrum added are shown in orange. Clustering information allows a better determination of $B_{sz}$ and $C_{sz}$. This partially breaks the degeneracy between these parameters, $w$ and $\Omega_M$, thereby tightening the final measurements of $w$ and $\Omega_M$.