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Paper IPM / Physic / 17663  


Abstract:  
Hubble tension is a problem in onedimensional (1D) posteriors, since local $H_0$ determinations are only sensitive to a single parameter. Projected 1D posteriors for $\Lambda$CDM cosmological parameters become more nonGaussian with increasing effective redshift when the model is fitted to redshift binned data in the late Universe. We explain mathematically why this nonGaussianity arises and show using observational Hubble data (OHD) that Markov Chain Monte Carlo (MCMC) marginalisation leads to 1D posteriors that fail to track the $\chi^2$ minimum at $68\%$ confidence level in high redshift bins.
To remedy this limitation of MCMC, we resort to profile distributions as a complementary technique. Doing so, we observe that $z \gtrsim 1$ cosmic chronometer (CC) data currently prefers a nonevolving (constant) Hubble parameter over a Planck$\Lambda$CDM cosmology at $\sim 2 \sigma$. Within the Hubble tension debate, it is imperative that subsamples of data sets with differing redshifts yield similar $H_0$ values. In addition, we confirm that MCMC degeneracies observed in 2D posteriors are not due to curves of constant $\chi^2$. Finally, on the assumption that the Planck$\Lambda$CDM cosmological model is correct, using profile distributions we confirm a $>2 \sigma$ discrepancy with Planck$\Lambda$CDM in a combination of CC and baryon acoustic oscillations (BAO) data beyond $ z \sim 1.5$. This confirms a discrepancy reported earlier with fresh methodology.
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