The available experimental data prefers plateau models of cosmic inflation, and among them Starobinsky inflation (aka R^2 inflation) is preferred, even if maybe not significantly. Since Starobinsky inflation is pure gravity (the inflaton field here is an effective incarnation of a higher gravitational curvature correction), it lends itself to embedding into supergravity models. There are some claims that the match of Starobsinsky inflation to data further improves after embedding into supergravity. For instance Alexandre-Houston-Mavromatos claim that under mild (?) assumptions gravitino condensation produces just the right Starobinsky potential (here), while Dalianis-Farakos claim that a problem with the size of the initial homogeneous patch goes away after embedding into supergravity (here). Clearly there are assumptions going into such statements. It would be good to have some feeling as to how robust these are. Does anyone here have further insight on this? I'd be grateful for comments and pointers.