In this paper, we study a projectable Hořava-Lifshitz cosmology without the detailed balance condition minimally coupled to a nonlinear self-coupling scalar field. In the minisuperspace framework, the super-Hamiltonian of the presented model is constructed by means of which some classical solutions for the scale factor and scalar field are obtained. Since these solutions exhibit various types of singularities, we came up with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology. The resulting quantum wave functions are then used to investigate the possibility of the avoidance of classical singularities due to quantum effects which show themselves important near these singularities.

中文翻译：

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Hořava-Lifshitz标量场宇宙学：古典观点和量子观点

在本文中，我们研究了可预测的Hořava-Lifshitz宇宙学，而没有将详细的平衡条件最小化到非线性自耦合标量场的情况。在微型超空间框架中，构造了所提出模型的超哈密顿量，由此获得了比例因子和标量场的一些经典解。由于这些解决方案表现出各种类型的奇异性，因此我们在惠勒-德威特量子宇宙学方法的背景下提出了模型的量化方法。然后将所得的量子波函数用于研究避免经典奇异性的可能性，这是由于量子效应表明了它们在这些奇异性附近很重要。