Abstract We perform a detailed study of the integrability of the Hořava-Lifshitz scalar field cosmology in a Friedmann-Lemaître-Robertson-Walker background space-time. The approach we follow to determine the integrability is that of singularity analysis. More specifically, we test whether the gravitational field equations possess the Painlevé 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 a Laurent expansion and more specifically write the solution in terms of right Painlevé series.

中文翻译：

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Hořava-Lifshitz 标量场论中的宇宙学解

摘要 我们在弗里德曼-勒梅特-罗伯逊-沃克背景时空中详细研究了 Hořava-Lifshitz 标量场宇宙学的可积性。我们用来确定可积性的方法是奇异性分析。更具体地说，我们测试引力场方程是否具有 Painlevé 性质。对于标量场的指数势，我们能够对场方程进行解析显式积分，并根据 Laurent 展开式写出解，更具体地说，根据右 Painlevé 级数写出解。