Quantum cosmology with \(R+R^2\) gravity (Q2784141)

The authors discuss a cosmological model which in other places carries the name ``Starobinsky model''. It follows from a lagrangian being the sum of the Einstein-Hilbert term \(R\) and the curvature squared term \(R^2\) leading to fourth-order terms in the field equation. In the present paper, the related cosmological equations are quantized, thus leading to a model of quantum cosmology. The authors mention the non-uniqueness of the quantization procedure in dependence of how auxiliary variables are introduced. The authors write in their abstract: `` \dots For the curvature squared term this technique yields, for the first time, a quantum mechanical probability interpretation of quantum cosmology \dots We conclude that the Einstein-Hilbert action should essentially be modified by, at least, a curvature squared term \dots '' Here the present reviewer would like to add: The authors have done a certain step towards a better understanding of these probabilities, but it is surely not for the first time that such an interpretation was given, see e.g. the references listed at the end of the paper.