In this paper, we discuss possible three early eras of the universe in the theoretical context of the Galilean cosmology. The first phase is a slow-roll inflation phase in which the friction term in the equations of motion dominates over the kinetic term. This is the initial vacuum state leading to quasi-de Sitter expansion. The second phase is where the cosmological perturbations are supposed to be generated. In this phase, the friction term is supposed to be negligible which leads to the appearance of the Galileon inflation field. The third phase is the reheating phase in the standard cosmology, where the oscillations of a canonical scalar field in the model lead to this phase. These three eras for the early universe are shown by a single master equation of the theory. However, we compute observational indices (the scalar spectral index parameter and the tensor-to-scalar ratio) for the era where the era that the perturbations are produced. Finally, we compare viability of the theoretical findings with the latest Planck observational data.

中文翻译：

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伽利略暴胀场与宇宙的三个黑暗时代

在本文中，我们在伽利略宇宙学的理论背景下讨论了宇宙可能的三个早期时代。第一阶段是缓慢滚动的膨胀阶段，其中运动方程中的摩擦项优于动力学项。这是导致准去西特膨胀的初始真空状态。第二阶段是应该产生宇宙学扰动的地方。在这个阶段，摩擦项应该可以忽略不计，这导致了伽利略暴胀场的出现。第三阶段是标准宇宙学中的再加热阶段，其中模型中的规范标量场的振荡导致该阶段。早期宇宙的这三个时代由一个单一的理论主方程显示。然而，我们计算产生扰动的时代的观测指数（标量光谱指数参数和张量与标量比）。最后，我们将理论发现的可行性与最新的普朗克观测数据进行了比较。