  Aims: We want to investigate the growth of bar instability in stellar disks
embedded in a suitable dark matter halo evolving in a fully consistent
cosmological framework.
  Methods: We perform seven cosmological simulations to emphasise the role of
both the disk-to-halo mass ratio and of the Toomre parameter, Q, on the
evolution of the disk.We also compare our fully cosmological cases with
corresponding isolated simulations where the same halo, is extracted from the
cosmological scenario and evolved in physical coordinates.
  Results: A long living bar, lasting about 10 Gyr, appears in all our
simulations. In particular, disks expected to be stable according to classical
criteria, form indeed weak bars. We argue that such a result is due to the
dynamical properties of our cosmological halo which is far from stability and
isotropy, typical of the classical halos used in literature; it is dynamically
active, endowed of substructures and infall.
  Conclusions: At least for mild self-gravitating disks, the study of the bar
instability using isolated isotropic halos, in gravitational equilibrium, can
lead to misleading results. Furthermore, the cosmological framework is needed
for quantitatively investigating such an instability.

Astrophysics