Cyclic Inflation
  We present an inflationary model that is geodesically complete and does not suffer from the transplanckian problem. In most inflationary models, massless (conformal) scalar field fluctuations in a deSitter background gives rise to a scale-invariant spectrum. In this work, we realize scale invariant perturbations from thermal fluctuations in (conformal) radiation during a radiation dominated contraction era prior to inflation. As the modes exit the Hubble radius during the contraction phase, scale invariant fluctuations are indeed generated. After many cycles, we enter into a power-law inflationary phase, that stretches the modes produced in the previous contraction phase to scales that we observe today. 
Tirthabir Biswas and Stephon Alexander