  We present the first numerical simulations in coupled dark energy cosmologies
with high enough resolution to investigate the effects of the coupling on
galactic and sub-galactic scales. We choose two constant couplings and a
time-varying coupling function and we run simulations of three Milky-Way-size
halos ($\sim$10$^{12}$M$_{\odot}$), a lower mass halo
(6$\times$10$^{11}$M$_{\odot}$) and a dwarf galaxy halo
(5$\times$10$^{9}$M$_{\odot}$). We resolve each halo with several millions dark
matter particles. On all scales the coupling causes lower halo concentrations
and a reduced number of substructures with respect to LCDM. We show that the
reduced concentrations are not due to different formation times, but they are
related to the extra terms that appear in the equations describing the
gravitational dynamics. On the scale of the Milky Way satellites, we show that
the lower concentrations can help in reconciling observed and simulated
rotation curves, but the coupling values necessary to have a significant
difference from LCDM are outside the current observational constraints. On the
other hand, if other modifications to the standard model allowing a higher
coupling (e.g. massive neutrinos) are considered, coupled dark energy can
become an interesting scenario to alleviate the small-scale issues of the LCDM
model.
