  We discuss some aspects of the Horava-Lifshitz cosmology with different
matter components considered as dominants at different stages of the cosmic
evolution (each stage is represented by an equation of state
pressure/density=constant). We compare cosmological solutions from this theory
with their counterparts of General Relativity (Friedmann cosmology). At early
times, the Horava- Lifshitz cosmology contains a curvature-dependent dominant
term which is stiff matter-reminiscent and this fact motivates to discuss, in
some detail, this term beside the usual stiff matter component
(pressure=density) if we are thinking in the role that this fluid could have
played early in the framework of the holographic cosmology. Nevertheless, we
show that an early stiff matter component is of little relevance in
Horava-Lifshitz cosmology.
