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We introduce a new framework for quantifying correlated uncertainties of theinfinite-matter equation of state derived from chiral effective field theory($\chi$EFT). Bayesian machine learning via Gaussian processes withphysics-based hyperparameters allows us to efficiently quantify and propagatetheoretical uncertainties of the equation of state, such as $\chi$EFTtruncation errors, to derived quantities. We apply this framework tostate-of-the-art many-body perturbation theory calculations withnucleon-nucleon and three-nucleon interactions up to fourth order in the$\chi$EFT expansion. This produces the first statistically robust uncertaintyestimates for key quantities of neutron stars. We give results up to twicenuclear saturation density for the energy per particle, pressure, and speed ofsound of neutron matter, as well as for the nuclear symmetry energy and itsderivative. At nuclear saturation density the predicted symmetry energy and itsslope are consistent with experimental constraints.

How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties