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Standard cosmology has many successes on large scales, but faces somefundamental difficulties on small, galactic scales. One such difficulty is thecusp/core problem. High resolution observations of the rotation curves for darkmatter dominated low surface brightness (LSB) galaxies imply that galactic darkmatter halos have a density profile with a flat central core, whereas N-bodystructure formation simulations predict a divergent (cuspy) density profile atthe center. It has been proposed that this problem can be resolved by stellarfeedback driving turbulent gas motion that erases the initial cusp. However,strong gravitational lensing prefers a cuspy density profile for galactichalos. In this paper, we use the most recent high resolution observations ofthe rotation curves of LSB galaxies to fit the core size as a function of halomass, and compare the resultant lensing probability to the observationalresults for the well defined combined sample of the Cosmic Lens All-Sky Survey(CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS). Thelensing probabilities based on such density profiles are too low to match theobserved lensing in CLASS/JVAS. High baryon densities in the galaxies thatdominate the lensing statistics can reconcile this discrepancy, but only ifthey steepen the mass profile rather than making it more shallow. This placescontradictory demands upon the effects of baryons on the central mass profilesof galaxies.

Contradiction between strong lensing statistics and a feedback solution to the cusp/core problem