A simple way to construct models with early cosmological Genesis epoch is to employ bosonic fields whose Lagrangians transform homogeneously under scaling transformation. We show that in these theories, for a range of parameters defining the Lagrangian, there exists a homogeneous power-law solution in flat space-time, whose energy density vanishes, while pressure is negative (power-law Genesis). We find the condition for the legitimacy of the classical field theory description of such a situation. We note that this condition does not hold for our earlier Genesis model with vector field. We construct another model with vector field and power-law background solution in flat space-time, which is legitimately treated within classical field theory, violates the Null Energy Condition (NEC) and is stable. Upon turning on gravity, this model describes the early Genesis stage.

中文翻译：

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幂律起源：强耦合和类伽利略矢量场

构建具有早期宇宙学创世纪元的模型的一种简单方法是使用玻色子场，其拉格朗日量在标度变换下均匀变换。我们表明，在这些理论中，对于定义拉格朗日函数的一系列参数，在平坦时空中存在一个齐次幂律解，其能量密度为零，而压力为负（幂律创世纪）。我们找到了经典场论描述这种情况的合法性条件。我们注意到这个条件不适用于我们早期的带有矢量场的创世纪模型。我们在平面时空中构造了另一个具有矢量场和幂律背景解的模型，该模型在经典场论中得到了合理的处理，违反了零能量条件（NEC）并且是稳定的。开启重力后，