Using state-of-the-art adaptive mesh refinement cosmological hydrodynamic simulations with a spatial resolution of proper 0.21kpc/h in refined subregions embedded within a comoving cosmological volume (27.4Mpc/h)^3, we investigate the sizes of galaxies at z=3 in the standard cold dark matter model where reionization is assumed to complete at zri~6. Our simulated galaxies are found to be significantly smaller than the observed ones: while more than one half of the galaxies observed by HST and VLT ranging from rest-frame UV to optical bands with stellar masses larger than 2E10 Msun have half-light radii larger than 2kpc/h, none of the simulated massive galaxies in the same mass range have half-light radii larger than 2kpc/h, after taking into account dust extinction. Corroborative evidence is provided by the rotation curves of the simulated galaxies with total masses of 1E11-1E12Msun, which display values 300-1000km/s at small radii (0.5kpc/h) due to high stellar concentration in the central regions, larger than those of any well observed galaxies. Possible physical mechanisms to resolve this serious problem include: (1) an early reionization at zri>>6 to suppress gas condensation hence star formation, (2) a strong, internal energetic feedback from stars or central black holes to reduce the overall star formation efficiency, or (3) a substantial small-scale cutoff in the matter power spectrum.

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