Tröster, Tilman, Asgari, Marika, Blake, Chris, Cataneo, Matteo, Heymans, Catherine, Hildebrandt, Hendrik, Joachimi, Benjamin, Lin, Chieh-An, Sánchez, Ariel G., Wright, Angus H., Bilicki, Maciej, Bose, Benjamin, Crocce, Martin, Dvornik, Andrej, Erben, Thomas, Giblin, Benjamin, Glazebrook, Karl, Hoekstra, Henk, Joudaki, Shahab, Kannawadi, Arun, Köhlinger, Fabian, Kuijken, Konrad, Lidman, Chris, Lombriser, Lucas, Mead, Alexander, Parkinson, David, Shan, HuanYuan, Wolf, Christian, Xia, Qianli, Tröster, Tilman, Asgari, Marika, Blake, Chris, Cataneo, Matteo, Heymans, Catherine, Hildebrandt, Hendrik, Joachimi, Benjamin, Lin, Chieh-An, Sánchez, Ariel G., Wright, Angus H., Bilicki, Maciej, Bose, Benjamin, Crocce, Martin, Dvornik, Andrej, Erben, Thomas, Giblin, Benjamin, Glazebrook, Karl, Hoekstra, Henk, Joudaki, Shahab, Kannawadi, Arun, Köhlinger, Fabian, Kuijken, Konrad, Lidman, Chris, Lombriser, Lucas, Mead, Alexander, Parkinson, David, Shan, HuanYuan, Wolf, Christian, and Xia, Qianli
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 $S_8=0.779^{+0.013}_{-0.013}$., Comment: 15 pages, 9 figures, 3 tables, accepted in A&A. This paper concludes the KiDS-1000 series of papers: Heymans, Tr\"oster et al. (arXiv:2007.15632), Asgari et al. (arXiv:2007.15633), Hildebrandt et al. (arXiv:2007.15635), Joachimi et al. (arXiv:2007.01844), and Giblin et al. (arXiv:2007.01845). Data products, likelihoods, and posteriors can be found http://kids.strw.leidenuniv.nl/DR4/lensing.php