  The properties of symmetric nuclear and pure neutron matter are investigated
within an extended self-consistent Green's function method that includes the
effects of three-body forces. We use the ladder approximation for the study of
infinite nuclear matter and incorporate the three-body interaction by means of
a density-dependent two-body force. This force is obtained via a correlated
average over the third particle, with an in-medium propagator consistent with
the many-body calculation we perform. We analyze different prescriptions in the
construction of the average and conclude that correlations provide small
modifications at the level of the density-dependent force. Microscopic as well
as bulk properties are studied, focusing on the changes introduced by the
density dependent two-body force. The total energy of the system is obtained by
means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate
previously used uncorrelated averages and extend the availability of chirally
motivated forces to a larger density regime.
