We study a toy model of continuous infinite expansion of space-time with the flat start. We use as the gravitational background a conformally flat metric with an exponentially growing factor in conformal time. We aim to clarify some properties of quantum fields in such a gravitational background. In particular, we calculate one-loop corrections to the Keldysh propagator to verify the fact of secular growth of the occupation number and anomalous quantum average in the massless scalar field theory with self-interactions. We perform the calculation in arbitrary dimensions with the use of the Schwinger-Keldysh technique. We get a secular growth that is not of a kinetic type. We provide some results for the case of generic interaction $\frac{\lambda }{b!}{\varphi }^b$.

中文翻译：

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量子修正与永恒膨胀宇宙中物质应力-能量张量的相关性

我们研究了一个平坦开始的时空连续无限膨胀的玩具模型。我们使用共形平坦度量作为引力背景，其共形时间中的因子呈指数增长。我们的目标是阐明在这种引力背景下量子场的一些性质。特别是，我们计算了对凯尔迪什传播器的单环修正，以验证具有自相互作用的无质量标量场理论中占据数的长期增长和反常量子平均的事实。我们使用 Schwinger-Keldysh 技术在任意维度上进行计算。我们得到的是非动力型的长期增长。我们提供了通用交互情况的一些结果$\frac{\lambda }{乙！}{\phi }^{乙}$。