Cosmological solutions in Ho\v{r}ava-Lifshitz gravity

We perform a detailed study on the integrability of the Ho\v{r}% ava-Lifshitz scalar field cosmology in a Friedmann–Lema^{\i}% tre–Robertson–Walker background spacetime. The approach we follow to determine the integrability is that of the Singularity Analysis. More specifically, we test if the gravitational field equations possesses the Painlev'{e} property. For the exponential potential of the scalar field we are able to perform an analytic explicit integration of the field equations and write the solution in terms of Laurent expansion and more specifically write the solution in terms of Right Painlev'{e} series.