The interpretation of upcoming weak gravitational lensing surveys depends critically on our understanding of the matter power spectrum on scales k < 10 h Mpc −1 , where baryonic processes are important. In this paper we study the impact of gas flows associated with galaxy formation on the matter power spectrum using a halo model that treats the stars and gas separately from the dark matter distribution. The baryonic components are constrained empirically: the hot gas using fits to X-ray observations of groups and clusters of galaxies, and the stellar component using a halo occupation distribution. Since X-ray observations cannot generally measure the hot gas content outside r 500c , we vary the gas density profiles beyond this radius. Compared with dark matter only models, we find a total power suppression of 1 % (5 %) on scales 0.2 − 1 h Mpc −1 (0.5 − 2 h Mpc −1 ), where lower baryon fractions result in stronger suppression. We show that groups of galaxies (10 13 < m 500c /(h −1 M ) < 10 14 ) dominate the total power at all scales k 10 h Mpc −1 . We illustrate the importance of measuring accurate halo masses by comparing models that do and do not account for a hydrostatic bias of 1−b = 0.7 in the halo masses from X-ray observations. We find that using biased halo masses results in an underestimation of the power suppression of up to 4 % at k = 1 h Mpc −1 . Contrary to work based on hydrodynamical simulations, our conclusion that baryonic effects can no longer be neglected is not subject to uncertainties associated with our poor understanding of feedback processes. Our findings highlight the need for observations to probe the outskirts of groups and clusters since these observations are the most constraining for the power suppression on scales k 1 h Mpc −1 .

We quantify two main pathways through which baryonic physics biases cluster count cosmology. We create mock cluster samples that reproduce the baryon content inferred from X-ray observations. We link clusters to their counterparts in a dark matter-only universe, whose abundances can be predicted robustly, by assuming the dark matter density profile is not significantly affected by baryons. We derive weak lensing halo masses and infer the best-fitting cosmological parameters Ωm, S8 = σ8(Ωm/0.3)0.2, and w0 from the mock cluster sample. We find that because of the need to accommodate the change in the density profile due to the ejection of baryons, weak lensing mass calibrations are only unbiased if the concentration is left free when fitting the reduced shear with NFW profiles. However, even unbiased total mass estimates give rise to biased cosmological parameters if the measured mass functions are compared with predictions from dark matter-only simulations. This bias dominates for haloes with m500c &lt; 1014.5 h−1 M⊙. For a stage IV-like cluster survey without mass estimation uncertainties, an area ≈15000 deg2 and a constant mass cut of m200m, min = 1014 h−1 M⊙, the biases are −11 ± 1 per cent in Ωm, −3.29 ± 0.04 per cent in S8, and 9 ± 1.5 per cent in w0. The statistical significance of the baryonic bias depends on how accurately the actual uncertainty on individual cluster mass estimates is known. We suggest that rather than the total halo mass, the (re-scaled) dark matter mass inferred from the combination of weak lensing and observations of the hot gas, should be used for cluster count cosmology.

The abundance of clusters of galaxies is highly sensitive to the late-time evolution of the matter distribution, since clusters form at the highest density peaks. However, the 3D cluster mass cannot be inferred without deprojecting the observations, introducing model-dependent biases and uncertainties due to the mismatch between the assumed and the true cluster density profile and the neglected matter along the sightline. Since projected aperture masses can be measured directly in simulations and observationally through weak lensing, we argue that they are better suited for cluster cosmology. Using the Mira–Titan suite of gravity-only simulations, we show that aperture masses correlate strongly with 3D halo masses, albeit with large intrinsic scatter due to the varying matter distribution along the sightline. Nonetheless, aperture masses can be measured ≈2 − 3 times more precisely from observations, since they do not require assumptions about the density profile and are only affected by the shape noise in the weak lensing measurements. We emulate the cosmology dependence of the aperture mass function directly with a Gaussian process. Comparing the cosmology sensitivity of the aperture mass function and the 3D halo mass function for a fixed survey solid angle and redshift interval, we find the aperture mass sensitivity is higher for Ωm and wa, similar for σ8, ns, and w0, and slightly lower for h. With a carefully calibrated aperture mass function emulator, cluster cosmology analyses can use cluster aperture masses directly, reducing the sensitivity to model-dependent mass calibration biases and uncertainties.

Systematic uncertainties in the mass measurement of galaxy clusters limit the cosmological constraining power of future surveys that will detect more than 105 clusters. Previously, we argued that aperture masses can be inferred more accurately and precisely than 3D masses without loss of cosmological constraining power. Here, we use the Baryons and Haloes of Massive Systems (BAHAMAS) cosmological, hydrodynamical simulations to show that aperture masses are also less sensitive to changes in mass caused by galaxy formation processes. For haloes with m200m, dmo &gt; 1014 h−1 M⊙, binned by their 3D halo mass, baryonic physics affects aperture masses and 3D halo masses similarly when measured within apertures similar to the halo virial radius, reaching a maximum reduction of ≈3 per cent. For lower-mass haloes, 1013.5 &lt; m200m, dmo/h−1 M⊙ &lt; 1014, and aperture sizes ∼1 h−1 cMpc, representative of weak lensing observations, the aperture mass is consistently reduced less (≲ 5 per cent) than the 3D halo mass (≲ 10 per cent for m200m). The halo mass reduction evolves only slightly, by up to 2 per centage points, between redshift 0.25 and 1 for both the aperture mass and m200m. Varying the simulated feedback strength so the mean simulated hot gas fraction covers the observed scatter inferred from X-ray observations, we find that the aperture mass is consistently less biased than the 3D halo mass, by up to 2 per centage points at m200m, dmo = 1014 h−1 M⊙. Therefore, aperture mass calibrations provide a fruitful path to reduce the sensitivity of future cluster surveys to systematic uncertainties.