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By adding a three dimensional manifold to an eleven dimensional manifold insupergravity, we obtain the action of $F(R)$-gravity and find that it isanomaly free. We calculate the scale factor of the inflationary universe inthis model, and observe that it is related to the slow-roll parameters. Thescalar-tensor ratio R\_(scalar-tensor) is in good agreement with experimentaldata.

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