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We investigate the validity of a \emph{minimal} cosmological model derivedfrom the renormalizable Ho$\check{\textrm{r}}$ava action at low redshift scalesby using different cosmological and statistical tests. Assuming pure attractivegravity, i.e., $\lambda>1/3$ in the Ho$\check{\textrm{r}}$ava action, wecompare the Union 2.1 supernova type Ia data with the kinematics following froma model-independent approach. The two approaches, although compatible, lead toexplicit cosmographic constraints on the free parameters of theHo$\check{\textrm{r}}$ava action, which turn out to be in strong disagreementwith the $\Lambda$CDM, $w$CDM and Chevallier-Polarski-Linder scenarios. To showthis, we use standard diagnostic tools of regression models, namely the Akaikeand the Bayesian Information Criteria. Using such model-independent statisticalmethods, we show that Ho$\check{\textrm{r}}$ava-Lifshitz cosmology differs fromthe standard dark energy scenarios, \emph{independently} of the number of freeparameters involved in the model. Since this result is valid at small redshiftdomains, it indicates the presence of inconsistencies in the minimal version ofHo$\check{\textrm{r}}$ava-Lifshitz cosmology even at the level of backgroundcosmology.

Kinematic and statistical inconsistencies of Ho$\check{\textrm{r}}$ava-Lifshitz cosmology