Inflationary Brans-Dicke quantum universe

The formulation of Brans-Dicke (BD) gravity with matter in the Einstein frame is realized as Einstein gravity with dilaton and dilaton coupled matter. We calculate the one-loop 4d anomaly-induced effective action (EA) due to N dilaton coupled massless fermions on the time dependent conformally flat background with non-trivial dilaton. Using such (complete) effective action, the (fourth-order) quantum-corrected equations of motion are derived. One special solution of these equations representing an inflationary Universe (with exponential scale factor) and (much slower) expanding BD dilaton is given. Similarly, 2d quantum BD Universe with time-dependent dilaton is constructed. In the last case, the dynamics is completely due to quantum effects.