Inflation without self-reproduction in $F(R)$ gravity
  We investigate inflation in frames of two classes of $F(R)$ gravity and check its consistency with Planck data. It is shown that $F(R)$ inflation without self-reproduction may be constructed in close analogy with the corresponding scalar example proposed by Mukhanov for the resolution the problems of multiverse, predictability and initial conditions. 
Shin'ichi Nojiri and Sergei D. Odintsov
gr-qc astro-ph.CO hep-th