The standard model of cosmology is founded on the basis that the expansion rate of the universe is accelerating at present --- as was inferred originally from the Hubble diagram of Type Ia supernovae. There exists now a much bigger database of supern
ovae so we can perform rigorous statistical tests to check whether these standardisable candles indeed indicate cosmic acceleration. Taking account of the empirical procedure by which corrections are made to their absolute magnitudes to allow for the varying shape of the light curve and extinction by dust, we find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion.
We consider two approaches to estimate and characterise the theoretical uncertainties stemming from the missing higher orders in perturbative calculations in Quantum Chromodynamics: the traditional one based on renormalisation and factorisation scale
variation, and the Bayesian framework proposed by Cacciari and Houdeau. We estimate uncertainties with these two methods for a comprehensive set of more than thirty different observables computed in perturbative Quantum Chromodynamics, and we discuss their performance in properly estimating the size of the higher order terms that are known. We find that scale variation with the conventional choice of varying scales within a factor of two of a central scale gives uncertainty intervals that tend to be somewhat too small to be interpretable as 68% confidence-level-heuristic ones. We propose a modified version of the Bayesian approach of Cacciari and Houdeau which performs well for non-hadronic observables and, after an appropriate choice of the relevant expansion parameter for the perturbative series, for hadronic ones too.
