# Including massive neutrinos in thermal Sunyaev Zeldovich power spectrum and cluster counts analyses

## TL;DR

This paper incorporates massive neutrinos into SZ power spectrum and cluster count analyses, revealing subtle effects on cosmological constraints and proposing methods for improved neutrino mass measurements and intra-cluster medium characterization.

## Contribution

It provides a consistent framework for including neutrino effects in SZ analyses and explores the impact on cosmological parameter constraints and future measurement prospects.

## Key findings

- Including neutrinos causes a 0.25% downward shift in σ8 constraints.
- Constraints are consistent with other surveys under realistic mass bias assumptions.
- SZ power spectrum can potentially measure intra-cluster medium properties with high precision.

## Abstract

We consistently include the effect of massive neutrinos in the thermal Sunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlighting subtle dependencies on the total neutrino mass and data combination. In particular, we find that using the transfer functions for Cold Dark Matter (CDM) + baryons in the computation of the halo mass function, instead of the transfer functions including neutrino perturbations, as prescribed in recent work, yields a $\approx$ 0.25\% downward shift of the $\sigma_8$ constraint from tSZ power spectrum data, with a fiducial neutrino mass $\Sigma m_\nu=0.06$ eV. In $\Lambda$CDM, with an X-ray mass bias corresponding to the expected hydrostatic mass bias, i.e., $(1-b)\simeq0.8$, our constraints from Planck SZ data are consistent with the latest results from SPT, DES-Y1 and KiDS+VIKING-450. In $\nu\Lambda$CDM, our joint analyses of Planck SZ with Planck 2015 primary CMB yield a small improvement on the total neutrino mass bound compared to the Planck 2015 primary CMB constraint, as well as $(1-b)=0.64\pm0.04$~(68\%~CL). For forecasts, we find that competitive neutrino mass measurements using cosmic variance limited SZ power spectrum require masking the heaviest clusters and probing the small-scale SZ power spectrum up to $\ell_\mathrm{max}\approx10^4$. Although this is challenging, we find that SZ power spectrum can realistically be used to tightly constrain intra-cluster medium properties: we forecast a 2\% determination of the X-ray mass bias by combining CMB-S4 and our mock SZ power spectrum with $\ell_\mathrm{max}=10^3$.