Cold dark matter halos and cusps Cold dark matter is one of the preferred candidates for dark matter. Yet, models such as the NFW and isothermal predict that halos will contain cusps, where the density tends towards infinity, despite a finite mass of dark matter. Does CDM agree/disagree with this, and why?
 A: It's an open question. For a short review, click here. 
To give a bit of background; currently it seems that observations of dark matter density profiles in low-mass galaxies favour cored profile (where density reaches some smooth constant density close to the center), whereas N-body simulations favour a cuspy profile closer to the NFW profile (where density increases rapidly close to the centers of the galaxies). So the big question is of course how to explain this discrepancy.
Now there is a lot of debate to see what causes these cores which are not predicted by N-body simulations. The currently favoured explanations are:


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*N-body simulations are wrong and the cores can be explained by baryonic physics

*Cores are caused by dark matter particle nature


N-body is incorrect, and the explanation is baryonic physics
So the premise of this theory is that the N-body simulations are insufficient to describe the full dynamics of galaxy formation and evolution. This is fairly understandable, as most N-body simulations do not include baryonic physics at all. The ones that do include baryonic physics make a mountain of approximations in doing so.
One possible way to explain the discrepancy between the simulations and observations is to study the effects of baryonic physics and other physics not considered in N-body simulations. For example, so-called AGN feedback and supernovae explosions could heat up and give energy to the surrounding baryonic matter in the core of galaxies, which in turn would transfer some of that energy to dark matter via gravitational interaction. It has also been suggested that merger events could cause heating of the central core, which in would smoothen a cuspy profile, potentially creating a dark matter core.
Modifications to the dark matter particle nature
Alright so here, scientists hypothesize that perhaps N-body simulations are correct but the missing component comes from particle physics. Perhaps due to the particle nature of dark matter the cores could be caused by e.g. uncertainty principle. This model usually assumes that dark matter is produced non-thermally and is an ultralight bosonic particle (mass around $\approx 10^{-23}eV$). Because of this, the de broglie wavelength of the particle is so huge that dark matter has non-negligible quantum effects (quantum interference) on larger scales, potentially causing cored distributions in smaller galaxies.
