Geometry versus growth

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