  A density-dependent effective potential for the baryon-baryon interaction in
the presence of the (hyper)nuclear medium is constructed, based on the leading
(irreducible) three-baryon forces derived within SU(3) chiral effective field
theory. We evaluate the contributions from three classes: contact terms,
one-pion exchange and two-pion exchange. In the strangeness-zero sector we
recover the known result for the in-medium nucleon-nucleon interaction.
Explicit expressions for the Lambda-nucleon in-medium potential in (asymmetric)
nuclear matter are presented. Our results are suitable for implementation into
calculations of (hyper)nuclear matter. In order to estimate the low-energy
constants of the leading three-baryon forces we introduce the decuplet baryons
as explicit degrees of freedom and construct the relevant terms in the minimal
non-relativistic Lagrangian. With these, the constants are estimated through
decuplet saturation. Utilizing this approximation we provide numerical results
for the effect of the three-body force in symmetric nuclear matter and pure
neutron matter on the Lambda-nucleon interaction. A moderate repulsion that
increases with density is found in comparison to the free Lambda-nucleon
interaction.
