Putting Flat $\Lambda$CDM In The (Redshift) Bin

Flat $\Lambda$CDM cosmology is specified by two constant fitting parameters at the background level in the late Universe, the Hubble constant $H_0$ and matter density (today) $\Omega_m$. Mathematically, $H_0$ and $\Omega_m$ are either integration constants arising from solving ordinary differential equations or are directly related to integration constants. Seen in this context, if fits of the $\Lambda$CDM model to cosmological probes at different redshifts lead to different $(H_0, \Omega_m)$ parameters, this is a mismatch between mathematics and observation. Here, in mock observational Hubble data (OHD) (geometric probes of expansion history) we demonstrate evolution in distributions of best fit parameters with effective redshift. As a result, considerably different $(H_0, \Omega_m)$ best fits from Planck-$\Lambda$CDM cannot be precluded in high redshift bins. We explore if OHD, Type Ia supernovae and standardisable quasar samples exhibit redshift evolution of best fit $\Lambda$CDM parameters. In all samples, we confirm a decreasing $H_0$ and increasing $\Omega_m$ trend with increasing bin redshift. Through comparison with mocks, we confirm that similar behaviour can arise randomly within the flat $\Lambda$CDM model with probabilities as low as $p = 0.0021$ ($3.1 \, \sigma$). We present complementary profile distribution analysis confirming the shifts in cosmological parameters in high redshift bins. In particular, we identify a redshift range where Planck $(H_0, \Omega_m)$ values are disfavoured at $99.6 \%$ ($2.9 \sigma$) confidence level in a combination of OHD and supernovae data.