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 \(\Lambda \)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-\(\Lambda \)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 likelihoods 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.