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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.02129
- arXiv:
- arXiv:2211.02129
- Bibcode:
- 2022arXiv221102129C
- Keywords:
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- Astrophysics - Cosmology and Nongalactic Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 6 pages, 9 figures