High Redshift $\Lambda$CDM Cosmology: To Bin or not to Bin?

Understand

We construct observational Hubble $H(z)$ and angular diameter distance $D_{A}(z)$ mock data with baseline Planck $\Lambda$CDM input values, before fitting the $\Lambda$CDM model to study evolution of probability density functions (PDFs) of best fit cosmological parameters $(H_0, \Omega_m, \Omega_k)$ across redshift bins.

• We find that PDF peaks only agree with the input parameters in low redshift ($z \lesssim 1$) bins for $H(z)$ and $D_{A}(z)$ constraints, and in all redshift bins when $H(z)$ and $D_{A}(z)$ constraints are combined.
• When input parameters are not recovered, we observe that PDFs exhibit non-Gaussian tails towards larger $\Omega_m$ values and shifts to (less pronounced) peaks at smaller $\Omega_m$ values.
• This flattening of the PDF is expected as $H(z)$ and $D_{A}(z)$ observations only constrain combinations of cosmological parameters at higher redshifts, so uniform PDFs are expected.