Inflation in Oscillating Universe
  We make use of possible high energy correction to the Friedmann equation to implement the bounce and study the behavior of massive scalar field before and after bounce semianalytically and numerically. We find that the slow-roll inflation can be preceded by the kinetic dominated contraction. During this process, the field initially in the bottom of its potential can be driven by the anti-frictional force resulted from the contraction and roll up its potential hill, and when it rolls down after the bounce, it can driven a period inflation. The required e-folds number during the inflation limits the energy scale of bounce. Further unlike that expected, the field during the contraction can not be driven to arbitrary large value, even though the bounce occurs at Planck scale. 
Yun-Song Piao and Yuan-Zhong Zhang