The recent Planck satellite combined with earlier results eliminate a wide spectrum of more complex inflationary models and favour models with a single scalar field, as reported in the analysis of the collaboration. More important, though, is that all the simplest inflation models are disfavoured by the data while the surviving models -- namely, those with plateau-like potentials -- are problematic. We discuss how the restriction to plateau-like models leads to three independent problems: it exacerbates both the initial conditions problem and the multiverse-unpredictability problem and it creates a new difficulty which we call the inflationary "unlikeliness problem." Finally, we comment on problems reconciling inflation with a standard model Higgs, as suggested by recent LHC results. In sum, we find that recent experimental data disfavours all the best-motivated inflationary scenarios and introduces new, serious difficulties that cut to the core of the inflationary paradigm. Forthcoming searches for B-modes, non-Gaussianity and new particles should be decisive.
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