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Starobinsky inflation and Supergravity

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I may not be aware of the very latest developments, but as far as I see, after a little BICEP2 hickup, the Starobinsky model of cosmic inflation (or the class of these models) is rather preferred by observational data. Is that (still) right?

It's curious, because several arguments (as behind the above link) seem to suggest  that Starobinsky inflation goes rather well along with supergravity and low energy supersymmetry breaking. 

This here is a vague question, just out of interest, sorry. I am wondering if any expert seeing this here might enjoy providing an update on the status of the models, particularly with respect to embedding into supergravity and superstring models.

asked Jan 20, 2015 in Phenomenology by Urs Schreiber (5,745 points) [ no revision ]
It is not clear who is right regarding Bicep2 data. The claims of error are political, and one should wait until a replication, results from Bicep2 in a different patch of sky, and also the Planck data, all agree with each other, with no dissenting opinion. Until that point, it is premature to reject the data of the Bicep folks because competitors say they missed a background which Bicep claims is irrelevent. It is possibly irrelevant, and possibly relevant, only a replication can tell. I don't know the status of Starobinski inflation given the new data, I just wanted to make sure that you are fair to everyone.
What I meant to express with the reference to BICEP2  -- but clearly didn't do well, for which I apologize -- is that while there was much excitement about the implications of the BICEP2 claim for fundamental physics, it is striking -- isn't it --  that the consequences of the Planck data without the BICEP2 claim are at least as exciting, if not more so. For some reason this receives much less attention, and hence my question as to what may be said here.. Namely, the Planck data drastically favors the Starobinsky model for inflation (it sits right there in the middle of Planck's preferred parameter range) and various arguments, that I tried to link to above, say that this model, in turn, favors supergravity. That seems remarkable. A hint for a primordial gravitational wave is neat, but we entirely expect such waves to be there. A real hint for supergravity however goes in the direction of actual new physics. Now of course it all depends on how much may really be inferred from the model. That's why I asked here, hoping that some expert might see this and give us an overview of the state of the Starobinsky art with respect to supergravity.

Update: the new joint BICEP/Planck data as well as the Planck 2015 data is out, and they confirm the Planck results from 2013: the model of inflation strongly preferred by the data is Starobinsky inflation.

Also the analysis by Dalianis-Farakos just came out arXiv:1502.01246. They argue that embedding the Starobinsky model into supergravity solves its remaining problem: the size of initial homogenous patch.

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