Low-energy limit in the anomaly-induced action and the semiclassical cosmological bounce

Abstract

In the recently proposed scenario, the cosmological bounce occurs because the initially contracting Universe is not empty. In the region close to singularity, matter contents of the Universe heat up and effectively become radiation. Then, the trace anomaly automatically provides bounce if the overall beta function in the matter sector is positive. Independent of the remaining open questions on the quantum field theory side, it is interesting to consider this model from the cosmological perspective. In the present work, we develop the general formalism which is a necessary step for exploring the primordial cosmological perturbations. The main technical development is the formulation of the low-energy version for the nonlocal part of the effective action. The complete form of this action can be done local using two auxiliary scalars. In our new version, there are more scalars, but this enables one to avoid higher derivatives.