Understand
Recent local measurements of the Hubble constant made using supernovae have delivered a value that differs by $\sim$5$\sigma$ (statistical error) from predictions using the Cosmic Microwave Background (CMB), or using Baryon Acoustic Oscillations (BAO) and Big-Bang Nucleosynthesis (BBN) constraints, which are themselves consistent.
- The effective volume covered by the supernovae is small compared to the other probes, and it is therefore interesting to consider whether sample variance (often also called cosmic variance) is a significant contributor to the offset.
- We consider four ways of calculating the sample variance: (i) perturbation theory applied to the luminosity distance, which is the most common method considered in the literature; (ii) perturbation of cosmological parameters, as is commonly used to alleviate super-sample covariance in sets of N-body simulations; (iii) a new method based on the variance between perturbed spherical top-hat regions; (iv) using numerical N-body simulations.
- All give consistent results showing that, for the Pantheon supernova sample, sample variance can only lead to fluctuations in $H_0$ of order $\pm1$ km s$^{-1}$Mpc$^{-1}$ or less.