Inflationary Universe from Anomaly-Free F R

By adding a three-dimensional manifold to an eleven-dimensional manifold in supergravity, we obtain the action of $F\left(R\right)$ -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 tensor-scalar ratio $\left(R_{\text{tensor}-\text{scalar}}\right)$ is in good agreement with experimental data.