  We study the physics on the paramagnetic side of the phase diagram of the
cobaltates, $Na_{x}CoO_{2}$, with an implementation of cellular dynamical mean
field theory (CDMFT) with the non-crossing approximation (NCA) for the one-band
Hubbard model on a triangular lattice. At low doping we find that the low
energy physics is dominated by a quasi-dispersionless band. At half-filling, we
find a metal-insulator transition at $U_{c}=5.6\pm0.15t$ which depends weakly
on the cluster size. The onset of the metallic state occurs through the growth
of a coherence peak at the chemical potential. Away from half filling, in the
electron-doped regime, the system is metallic with a large, continuous Fermi
surface as seen experimentally. Upon hole doping, a quasi non-dispersing band
emerges at the top of the lower Hubbard band and controls the low-energy
physics. This band is a clear signature of non-Fermi liquid behavior and cannot
be captured by any weakly coupled approach. This quasi non-dispersive band,
which persists in a certain range of dopings, has been observed experimentally.
We also investigate the pseudogap phenomenon in the context of a triangular
lattice and we propose a new framework for discussing the pseudogap phenomena
in general. This framework involves a momentum-dependent characterization of
the low-energy physics and links the appearance of the pseudogap to a
reconstruction of the Fermi surface without invoking any long range order or
symmetry breaking. Within this framework we predict the existence of a
pseudogap for the two dimensional Hubbard model on a triangular lattice in the
weakly hole-doped regime.
