We present constraints on extensions to the flat \(\Lambda\)CDM cosmological model by varying the spatial curvature \(\Omega_K\), the sum of the neutrino masses \(\sum m_\nu\), the dark energy ...equation of state parameter \(w\), and the Hu-Sawicki \(f(R)\) gravity \(f_{R0}\) parameter. With the combined \(3\times2\)pt measurements of cosmic shear from the Kilo-Degree Survey (KiDS-1000), galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey (2dFLenS), we find results that are fully consistent with a flat \(\Lambda\)CDM model with \(\Omega_K=0.011^{+0.054}_{-0.057}\), \(\sum m_\nu<1.76\) eV (95% CL), and \(w=-0.99^{+0.11}_{-0.13}\). The \(f_{R0}\) parameter is unconstrained in our fully non-linear \(f(R)\) cosmic shear analysis. Considering three different model selection criteria, we find no clear preference for either the fiducial flat \(\Lambda\)CDM model or any of the considered extensions. Besides extensions to the flat \(\Lambda\)CDM parameter space, we also explore restrictions to common subsets of the flat \(\Lambda\)CDM parameter space by fixing the amplitude of the primordial power spectrum to the Planck best-fit value, as well as adding external data from supernovae and lensing of the CMB. Neither the beyond-\(\Lambda\)CDM models nor the imposed restrictions explored in this analysis are able to resolve the \(\sim 3\sigma\) tension in \(S_8\) between the \(3\times2\)pt constraints and Planck, with the exception of \(w\)CDM, where the \(S_8\) tension is resolved. The tension in the \(w\)CDM case persists, however, when considering the joint \(S_8\)-\(w\) parameter space. The joint flat \(\Lambda\)CDM CMB lensing and \(3\times2\)pt analysis is found to yield tight constraints on \(\Omega_{\rm m}=0.307^{+0.008}_{-0.013}\), \(\sigma_8=0.769^{+0.022}_{-0.010}\), and \(S_8=0.779^{+0.013}_{-0.013}\).
We measured the cross-correlation between galaxy weak lensing data from the Kilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB) lensing data from the Atacama Cosmology Telescope ...(ACT, DR4) and the Planck Legacy survey. We used two samples of source galaxies, selected with photometric redshifts, (0.1 z(B) 1.2) and (1.2 z(B) 2), which produce a combined detection significance of the CMB lensing and weak galaxy lensing cross-spectrum of 7.7σ. With the lower redshift galaxy sample, for which the cross-correlation was detected at a significance of 5.3σ, we present joint cosmological constraints on the matter density parameter, Ω(m), and the matter fluctuation amplitude parameter, σ(8), marginalising over three nuisance parameters that model our uncertainty in the redshift and shear calibration as well as the intrinsic alignment of galaxies. We find our measurement to be consistent with the best-fitting flat ΛCDM cosmological models from both Planck and KiDS-1000. We demonstrate the capacity of CMB weak lensing cross-correlations to set constraints on either the redshift or shear calibration by analysing a previously unused high-redshift KiDS galaxy sample (1.2 z(B) 2), with the cross-correlation detected at a significance of 7σ. This analysis provides an independent assessment for the accuracy of redshift measurements in a regime that is challenging to calibrate directly owing to known incompleteness in spectroscopic surveys.
