Because of the concerns just mentioned that CDM may predict higher densities and more substructure on small scales than is observed, many people have proposed alternatives to CDM. Two of these ideas that have been studied in the greatest detail are self-interacting dark matter (SIDM)  and warm dark matter (WDM).
Cold dark matter assumes that the dark matter particles have only weak interactions with each other and with other particles. SIDM assumes that the dark matter particles have strong elastic scattering cross sections, but negligible annihilation or dissipation. The hope was that SIDM might suppress the formation of the dense central regions of dark matter halos, although the large cross sections might also lead to high thermal conductivity which drains energy from halo centers and could lead to core collapse , and which also causes evaporation of galaxy halos in clusters, resulting in violation of the observed "fundamental plane" correlations . But in any case, self-interaction cross sections large enough to have a significant effect on the centers of galaxy-mass halos will make the centers of galaxy clusters more spherical [111, 112] and perhaps also less dense [113, 114] than gravitational lensing observations  indicate.
Warm dark matter arises in particle physics theories in which the dark matter particles have relatively high thermal velocities, for example because their mass is 1 keV , comparable to the temperature about a year after the Big Bang when the horizon first encompassed the amount of dark matter in a large galaxy. Such a velocity distribution can suppress the formation of structure on small scales. Indeed, this leads to constraints on how low the WDM particle mass can be. From the requirement that there is enough small-scale power in the linear power spectrum to reproduce the observed properties of the Ly forest in quasar spectra, it follows that this mass must exceed about 0.75 keV . The requirement that there be enough small halos to host early galaxies to produce the floor in metallicity observed in the Ly forest systems, and early galaxies and quasars to reionize the universe, probably implies a stronger lower limit on the WDM mass of at least 1 keV . Simulations [119, 120] do show that there will be far fewer small satellite halos with WDM than CDM. However, as I have already mentioned, inclusion of the effects of reionization may make the observed numbers of satellite galaxies consistent with the predictions of CDM , in which case WDM may predict too few small satellite galaxies. Lensing can be used to look for these subhalos [121, 122] and may already indicate that there are more of them than expected in WDM . Thus it appears likely that WDM does not solve all the problems it was invoked to solve, and may create new problems. Moreover, even with an initial power spectrum truncated on small scales, simulations appear to indicate that dark matter halos nevertheless have density profiles much like those in CDM [124, 68, 86] (although doubts have been expressed about the reliability of such simulations because of numerical relaxation ). But WDM does lead to lower concentration halos in better agreement with observed rotation velocity curves [126, 127].
One theoretical direction that does appear very much worth investigating is CDM with a tilt n ~ 0.9 in the primordial power spectrum Pp(k) kn . Such tCDM cosmology is favored by recent measurements of the power spectrum of the Ly forest  and appears to be consistent with the latest CMB measurements and all other available data . Our simple analytic model  predicts that the concentration of halos in tCDM will be approximately half that in LCDM, which appears to be true in a trial simulation by A. Kravtsov. While this does not resolve the cusp problem, it is a step in the right direction which may lessen the conflict with galaxy rotation curves.