  We study the Friedmann inflation in general covariant Horava-Lifshitz (HL)
gravity without the projectability conditions and with detailed and
non-detailed balance conditions. Accordingly, we derive modifications in the
Friedmann equations due to a single-scalar field potential describing
minimal-supersymmetrically extended inflation. By implementing two
time-independent equations of state (EoS) characterizing the cosmic background
geometry filled up with dark energy, the dependence of the tensorial and scalar
density fluctuations and their ratios on the inflation field are determined.
The latter refer to the time evolution of the inflationary field relative to
the Hubble parameter. Furthermore, the ratios of tensorial-to-spectral density
fluctuations are calculated in dependence on the spectral index. For cold dark
energy EoS $\omega=-1/3$, we find that the tensorial-to-spectral density
fluctuations are not depending on the different theories of gravity and the
results are very small relative to the recent BICEP2/Keck Array-Planck
observations, $10^{-9} \lessapprox r \lessapprox 10^{-3}$. We have also
calculated the tensorial and scalar perturbations of the primordial spectra.
