  We have performed both in-plane resistivity, Hall effect and specific heat
measurements on the thermoelectric cobalt oxide Ca$_{3}$Co$_{4}$O$_{9}$. Four
distinct transport regimes are found as a function of temperature,
corresponding to a low temperature insulating one up to $T_{min}\approx $63 K,
a strongly correlated Fermi liquid up to $T^*\approx $140 K, with
$\rho=\rho_0+AT^2$ and $A\approx 3.63$ $10^{-2} \mu \Omega cm/K^{2}$, followed
by an incoherent metal with $k_Fl\leq 1$ and a high temperature insulator above
T$^{**}\approx $510 K . Specific heat Sommerfeld coefficient $\gamma = 93$
mJ/(mol.K$^{2}$) confirms a rather large value of the electronic effective mass
and fulfils the Kadowaki-Woods ratio $A/\gamma^2 \approx 0.45$ 10$^{-5}$ $\mu
\Omega cm.K^2/(mJ^2mol^{-2})$. Resistivity measurements under pressure reveal a
decrease of the Fermi liquid transport coefficient A with an increase of $T^*$
as a function of pressure while the product $A(T^*)^2/a$ remains constant and
of order $h/e^2$. Both thermodynamic and transport properties suggest a strong
renormalization of the quasiparticles coherence scale of order $T^*$ that seems
to govern also thermopower.
