  We study Friedmann inflation in general Horava-Lifshitz (HL) gravity with
detailed and non-detailed but also without the projectability conditions.
Accordingly, we derive the modifications in the Friedmann equations due to
single scalar field potentials describing power-law and
minimal-supersymmetrically extended inflation. By implementing four types of
the equations-of-state charactering the cosmic background geometry, the
dependence of the tensorial and spectral density fluctuations and their ratio
on the inflation field is determined. The latter characterizes the time
evolution of the inflation field relative to the Hubble parameter. Furthermore,
the ratio of tensorial-to-spectral density fluctuations is calculated in
dependence on the spectral index. The resulting slow-roll parameters apparently
differ from the ones deduced from the standard General Relativity (Friedmann
gravity). We also observe that the tensorial-to-spectral density fluctuations
continuously decrease when moving from non-detailed HL gravity, to Friedmann
gravity, to HL gravity without the projectibility, and to detailed HL gravity.
This regular patter is valid for three types of cosmic equations-of-state and
different inflation potential models. The results fit well with the recent
PLANCK observations.
