  In this work we consider how the appearance of gradients of pseudoscalar
condensates in dense systems may possibly influence the transport properties of
photons in such a medium as well as other thermodynamic characteristics. We
adopt the hypothesis that in regions where the pseudoscalar density gradient is
large the properties of photons and fermions are governed by the usual
lagrangian extended with a Chern-Simons interaction for photons and a constant
axial field for fermions. We find that these new pieces in the lagrangian
produce non-trivial reflection coefficients both for photons and fermions when
entering or leaving a region where the pseudoscalar has a non-zero gradient. A
varying pseudoscalar density may also lead to instability of some fermion and
boson modes and modify some properties of the Fermi sea. We speculate that some
of these modifications could influence the cooling rate of stellar matter (for
instance in compact stars) and have other observable consequences. While
quantitative results may depend on precise astrophysical details most of the
consequences are quite universal and consideration should be given to this
possibility.
