A comparison of Bayesian and frequentist confidence intervals in the presence of a late Universe degeneracy

Abstract

Hubble tension is a problem in one-dimensional (1D) posteriors, since local $H_0$ determinations are only sensitive to a single parameter. Projected 1D posteriors for $\mathrm{\Lambda }$CDM cosmological parameters become more non-Gaussian with increasing effective redshift when the model is fitted to redshift-binned data in the late Universe. We explain mathematically why this non-Gaussianity 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 gain a second perspective, we resort to profile likelihoods as a complementary technique. Doing so, we observe that $z\gtrsim 1$ cosmic chronometer (CC) data currently prefer a non-evolving (constant) Hubble parameter over a Planck-$\mathrm{\Lambda }$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-$\mathrm{\Lambda }$CDM cosmological model is correct, using profile likelihoods we confirm a $>2\sigma$ discrepancy with Planck-$\mathrm{\Lambda }$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.