Bouncing inflation in a nonlinear R2+R4 gravitational model

We study a gravitational model with curvature-squared R2 and curvature-quartic R4 nonlinearities. The effective scalar degree of freedom ¿ (the scalaron) has a multivalued potential U(¿) consisting of a number of branches. These branches are fitted with each other in the branching and monotonic points. In the case of four-dimensional space-time, we show that the monotonic points are penetrable for the scalaron, while in the vicinity of the branching points, the scalaron has the bouncing behavior and cannot cross these points. Moreover, there are branching points where the scalaron bounces an infinite number of times with decreasing amplitude, and the Universe asymptotically approaches the de Sitter stage. Such accelerating behavior we call bouncing inflation. For this accelerating expansion, there is no need for original potential U(¿) to have a minimum or to check the slow-roll conditions. A necessary condition for such inflation is the existence of the branching points. This is a new type of inflation. We show that bouncing inflation takes place both in the Einstein and Brans-Dicke frames