Inflationary universe from anomaly-free $F(R)$-gravity

By adding a three dimensional manifold to an eleven dimensional manifold in supergravity, we obtain the action of $F(R)$-gravity and find that it is anomaly free. We calculate the scale factor of the inflationary universe in this model, and observe that it is related to the slow-roll parameters. The scalar-tensor ratio R_(scalar-tensor) is in good agreement with experimental data.