To explain the accelerated expansion of the late universe, the 1=R correction to Einstein gravity is usually considered, where R is the Ricci scalar. This correction term, if stable, is generally believed to be negligible during inflation. However, if the 1=R term is inflaton dependent, it will dramatically change the story of inflation. The entropy perturbation will naturally appear and drive the evolution of curvature perturbation outside the Hubble horizon. In a large class of models, the entropy perturbation can be made nearly scale invariant. In Einstein gravity the single-field inflation with a quartic potential has been ruled out by recent observations, but it revives when the 1=R term is turned on. The evolution of nonGaussianities on a large scale are also studied and applied to inflation with 1=R correction. In some specific models, a large non-Gaussianity can be naturally generated outside the horizon. A recent study ruled out almost all fðRÞ models during the matter-dominated phase. Taking this into consideration, we are left with a limited class of model which recovers the Einstein gravity soon after reheating.