Baryonic effects for weak lensing. Part II. Combination with X-ray data and extended cosmologies

An accurate modelling of baryonic feedback effects is required to exploit the full potential of future weak-lensing surveys such as Euclid or LSST . In this second paper in a series of two, we combine Euclid-like mock data of the cosmic shear power spectrum with an eROSITA X-ray mock of the cluster gas fraction to run a combined likelihood analysis including both cosmological and baryonic parameters. Following the first paper of this series, the baryonic effects (based on the baryonic correction model of ref. [1]) are included in both the tomographic power spectrum and the covariance matrix. However, this time we assume the more realistic case of a ΛCDM cosmology with massive neutrinos and we consider several extensions of the currently favoured cosmological model. For the standard ΛCDM case, we show that including X-ray data reduces the uncertainties on the sum of the neutrino mass by ~30 percent, while there is only a mild improvement on other parameters such as Ωm and σ8. As extensions of ΛCDM, we consider the cases of a dynamical dark energy model (wCDM), a f(R) gravity model (fRCDM), and a mixed dark matter model (ΛMDM) with both a cold and a warm/hot dark matter component. We find that combining weak-lensing with X-ray data only leads to a mild improvement of the constraints on the additional parameters of wCDM, while the improvement is more substantial for both fRCDM and ΛMDM . Ignoring baryonic effects in the analysis pipeline leads to significant false-detections of either phantom dark energy or a light subdominant dark matter component. Overall we conclude that for all cosmologies considered, a general parametrisation of baryonic effects is both necessary and sufficient to obtain tight constraints on cosmological parameters