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

Abstract

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. Our analysis leaves us with a choice to bin high redshift data in the knowledge that we may be unlikely to recover Planck values, or conduct full sample analysis that biases $\Lambda$CDM inferences to the lower redshift Universe.

6 pages, 9 figures; v2 typos corrected, to appear in Physics of the Dark Universe

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