Accelerating Hilbert-Einstein universe without dynamic dark energy

By using an unmodified Einstein gravity theory it is shown that all of the speeding-up effects taking place in the current universe are entirely due to the quantum effects associated with the background radiation or to the combination of such effects with those derived from the presence of a cosmological constant, without invoking any dynamic dark energy component. We obtain that in both cases the universe accelerates at a rate slightly beyond what is predicted by a cosmological constant but does not induce any big rip singularity in the finite future.