On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field

The anomaly-induced effective action is a useful tool for deriving the contributions coming from quantum effects of massless conformal fields. It is well known that such corrections in the higher derivative vacuum sector of the gravitational action provide the same exponential inflation (Starobinsky model) as the cosmological constant term. At the same time, the presence of a classical electromagnetic field breaks down the exponential solution. In this Letter we explore the role of the anomaly-induced term in the radiation sector and, furthermore, derive the “equation of state” and the scaling laws for all terms in the Einstein equations. As one could expect, the scaling law for the vacuum anomaly-induced effective action is the same as for the cosmological constant.