Fermi liquid theory of ultra-cold trapped Fermi gases: Extracting the Landau Parameters

We show how Fermi liquid theory can be applied to ultra-cold Fermi gases and propose a way to extract the position dependent effective mass and Landau parameters $F_{0}^{s}(r)$ and $F_{0}^{a}(r)$ from the experimental trap profiles, within the local density approximation. We outline the signatures for a Fermi liquid thereby addressing the recent claim that the normal state of a unitary gas is a Fermi liquid phase; this controversial claim counters other evidence for a non-Fermi liquid phase. Understanding these Fermi liquid signatures also bears on recent controversies over the nature of alternative ground states in a (possibly ferromagnetic) Fermi Hubbard gas.