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Abstract

Measurements of the gravitational constant $G$ are notoriously difficult.
Individual state-of-the-art experiments have managed to determine the value of
$G$ with high precision: although, when considered collectively, the range in
the measured values of $G$ far exceeds individual uncertainties, suggesting the
presence of unaccounted for systematic effects.
Here, we propose a Bayesian framework to account for the presence of
systematic errors in the various measurement of $G$ while proposing a consensus
value, following two paths: a parametric approach, based on the Maximum Entropy
Principle, and a non-parametric one, the latter being a very flexible approach
not committed to any specific functional form.
With both our methods, we find that the uncertainty on this fundamental
constant, once systematics are included, is significantly larger than what
quoted in CODATA 2018. Moreover, the morphology of the non-parametric
distribution hints towards the presence of several sources of unaccounted for
systematics. In light of this, we recommend a consensus value for the
gravitational constant $G = 6.6740^{+0.0015}_{-0.0015} \times 10^{-11}\
\mathrm{m}^3\ \mathrm{kg}^{-1}\ \mathrm{s}^{-2}$.