We examine some inflationary models based on modifications of gravity in the light of Planck 2015 data, such as the generalized Chaplygin inspired inflation, models based in N=1 supergravity and braneworld scenarios. We also show that, conversely, potentials with a very flat plateau yield a primordial spectrum similar to that of the Starobinsky model with no need to modify general relativity.
Gomes, C., Bertolami, O., & Rosa, J. G. (2018). Inflation with Planck data: A survey of some exotic inflationary models. Physical Review D, 97(10). https://doi.org/10.1103/PhysRevD.97.104061