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We compute from chiral two- and three-nucleon interactions the energy perparticle of symmetric nuclear matter and pure neutron matter at third-order inperturbation theory including self-consistent second-order single-particleenergies. Particular attention is paid to the third-order particle-holering-diagram, which is often neglected in microscopic calculations of theequation of state. We provide semi-analytic expressions for the direct termsfrom central and tensor model-type interactions that are useful as theoreticalbenchmarks. We investigate uncertainties arising from the order-by-orderconvergence in both many-body perturbation theory and the chiral expansion.Including also variations in the resolution scale at which nuclear forces areresolved, we provide new error bands on the equation of state, theisospin-asymmetry energy, and its slope parameter. We find in particular thatthe inclusion of third-order diagrams reduces the theoretical uncertainty atlow densities, while in general the largest error arises from omittedhigher-order terms in the chiral expansion of the nuclear forces.

Equation of state of nuclear and neutron matter at third-order in perturbation theory from chiral EFT