  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.
