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

## TL;DR

This paper investigates the integrability of Hořava-Lifshitz scalar field cosmology using Singularity Analysis, successfully deriving explicit solutions for exponential potentials through Painlevé series expansion.

## Contribution

It applies Singularity Analysis to Hořava-Lifshitz cosmology, providing explicit solutions and demonstrating integrability for exponential scalar field potentials.

## Key findings

- Successfully performed Painlevé analysis on the field equations.
- Derived explicit solutions in terms of Laurent and Painlevé series.
- Confirmed integrability for exponential potential cases.

## Abstract

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.