Relevance of quantum corrections to the matter stress-energy tensor in eternally expanding universes

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 $\frac{\lambda }{b!}{\varphi }^b$.

Figure 1

Diagrams of the first type.

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Diagrams of the second type.