Reconstruction of general relativistic cosmological solutions in modified gravity theories

We study the special class of exact solutions in cosmological models based on generalized scalar-tensor gravity with nonminimal coupling of a scalar field to the Ricci scalar and to the Gauss-Bonnet scalar in a 4D Friedmann universe corresponding to similar ones in GR. The parameters of cosmological perturbations in such models correspond to the case of Einstein gravity with a high precision. As an example of the proposed approach, we obtain the exact solutions for the power-law and exponential power-law inflation.