Geometry vs growth: Internal consistency of the flat ΛCDM model with KiDS-1000

We carry out a multi-probe self-consistency test of the flat $Λ$CDM model with the aim of exploring potential causes of the reported tensions between high- and low-redshift cosmological observations. We divide the model into two theory regimes determined by the smooth background (geometry) and the evolution of matter density fluctuations (growth), each governed by an independent set of Lambda Cold Dark Matter ($Λ$CDM) cosmological parameters. This extended model is constrained by a combination of weak gravitational lensing measurements from the Kilo-Degree Survey, galaxy clustering signatures extracted from Sloan Digital Sky Survey campaigns and the Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the primordial scalar fluctuation power spectrum measured in $\textit{Planck}$ cosmic microwave background (CMB) data. We find strong consistency between the geometry and growth parameters, and with the posterior of standard $Λ$CDM analysis. Tension in the amplitude of matter density fluctuations as measured by the parameter $S_8$ persists at around 3$σ$, with a $1.5\,\%$ constraint of $S_8 = 0.776_{-0.008}^{+0.016}$ for the combined probes. We also observe a less significant preference (at least $2σ$) for higher values of the Hubble constant, $H_0 = 70.5^{+0.7}_{-1.5}\,{\rm km\, s^{-1} Mpc^{-1}}$, as well as for lower values of the total matter density parameter $Ω_{\rm{m}} = 0.289^{+0.007}_{-0.005}$ compared to the full $\textit{Planck}$ analysis. Including the subset of the CMB information in the probe combination enhances these differences rather than alleviate them, which we link to the discrepancy between low and high multipoles in $\textit{Planck}$ data.