Spherical collapse and cluster number counts in DHOST theories that pass the constraints from gravitational waves

TL;DR

This paper studies how certain DHOST theories, consistent with gravitational wave constraints, affect galaxy cluster formation and counts, showing deviations from Einstein gravity influence structure growth and observable cluster abundance.

Contribution

It introduces a model of DHOST theories that pass gravitational wave constraints and analyzes their impact on spherical collapse and galaxy cluster counts.

Findings

Deviations from Einstein gravity suppress small-scale matter perturbations.

Cluster counts are reduced at high redshift with larger deviations.

Predicted counts are lower than ΛCDM, consistent with eROSITA survey data.

Abstract

We investigate the spherical collapse model and the abundance of galaxy clusters in a class of degenerate higher-order scalar--tensor (DHOST) theories in which gravitational waves do not decay into scalar perturbations and which are consistent with current constraints from gravitational-wave observations. We find that deviations from Einstein gravity can become significant at late times when the background universe is close to the scaling regime during the matter-dominated epoch. These deviations suppress the growth of linear matter perturbations on small scales while increasing the extrapolated linear density contrast at collapse, obtained from the spherical collapse model. Using the analytic mass function, we compute the corresponding cluster number counts. The minimum mass threshold in the mass integration for each redshift bin is determined by matching the predicted number counts in the $\Lambda$CDM model with those inferred from the eROSITA survey. We find that the cluster abundance reaches its maximum at low redshift bin, and that the number of clusters in the highest redshift bin is suppressed as the deviation from Einstein gravity becomes larger. The parameters of the theory are chosen such that the deviation from Einstein gravity at present is consistent with the local astrophysical bounds from binary pulsar observations. We find that even under such strict constraints, the upper bound on the deviation leads to lower predicted number counts compared with the $\Lambda$CDM model emulating the eROSITA survey results. However, this may be a consequence of the uncertainties in computing the number counts for the DHOST theories using the spherical collapse model and the analytical mass function.