Quantum Fluctuations and Eternal Inflation in the R²model

We show that in the R 2 inflationary model, as in the scalar field case, quantum fluctuations at early times can be sufficiently large that the universe evolves like a random walk. Within this picture we describe the resulting global structure of the universe: the so-called “eternal inflation” scenario. Such behavior can naturally fit into a picture of “quantum creation of the universe”. Inflating domains are present today and in fact are growing in number. Approximately every 10 −31 s new hot radiation dominated domains are created which occupy a volume larger than all the previously existing Friedmann universes; during the first ~10 −9 fraction of this period the power law expanding volume exceeds the inflating volume. Regularly, numerous domains occur where inflation proceeds purely classically and sufficiently to solve the problems of standard cosmology.