Relationship between the CMB, SZ Cluster Counts, and Local Hubble Parameter Measurements in a Simple Void Model

TL;DR

This paper explores whether a simple local void model can reconcile discrepancies between CMB, SZ cluster counts, and local Hubble measurements, finding that such a model predicts a local Hubble constant consistent with observations.

Contribution

It demonstrates that a simple void model can simultaneously explain CMB, SZ cluster counts, and local Hubble parameter measurements, providing a potential resolution to existing discrepancies.

Findings

Predicted local Hubble parameter $H_{loc}=70.1\,km/s/Mpc$ matches observations

A local under-dense region can reconcile SZ cluster counts with CMB data

The void model offers a consistent solution to multiple cosmological tensions.

Abstract

The discrepancy between the amplitudes of matter fluctuations inferred from Sunyaev-Zel'dovich (SZ) cluster number counts, the primary temperature, and the polarization anisotropies of the cosmic microwave background (CMB) measured by the Planck satellite can be reconciled if the local universe is embedded in an under-dense region as shown by Lee, 2014. Here using a simple void model assuming the open Friedmann-Robertson-Walker geometry and a Markov Chain Monte Carlo technique, we investigate how deep the local under-dense region needs to be to resolve this discrepancy. Such local void, if exists, predicts the local Hubble parameter value that is different from the global Hubble constant. We derive the posterior distribution of the local Hubble parameter from a joint fitting of the Planck CMB data and SZ cluster number counts assuming the simple void model. We show that the predicted local Hubble parameter value of $H_{\rm loc}=70.1\pm0.34~{\rm km\,s^{-1}Mpc^{-1}}$ is in better agreement with direct local Hubble parameter measurements, indicating that the local void model may provide a consistent solution to the cluster number counts and Hubble parameter discrepancies.