  Cosmological numerical simulations of galaxy formation have led to the cuspy
density profile of a pure cold dark matter halo toward the center, which is in
sharp contradiction with the observations of the rotation curves of cold dark
matter-dominated dwarf and low surface brightness disk galaxies, with the
latter tending to favor mass profiles with a flat central core. Many efforts
have been devoted to resolve this cusp-core problem in recent years, among
them, baryon-cold dark matter interactions are considered to be the main
physical mechanisms erasing the cold dark matter (CDM) cusp into a flat core in
the centers of all CDM halos. Clearly, baryon-cold dark matter interactions are
not customized only for CDM-dominated disk galaxies, but for all types,
including giant ellipticals. We first fit the most recent high resolution
observations of rotation curves with the Burkert profile, then use the
constrained core size-halo mass relation to calculate the lensing frequency,
and compare the predicted results with strong lensing observations.
Unfortunately, it turns out that the core size constrained from rotation curves
of disk galaxies cannot be extrapolated to giant ellipticals. We conclude that,
in the standard cosmological paradigm, baryon-cold dark matter interactions are
not universal mechanisms for galaxy formation, and therefore, they cannot be
true solutions to the cusp-core problem.
