  We use cosmic microwave background and large scale structure data to test a
broad and physically well-motivated class of inflationary models: those with
flat tree-level potentials (typical in supersymmetry). The non-trivial features
of the potential arise from radiative corrections which give a simple
logarithmic dependence on the inflaton field, making the models very
predictive. We also consider a modified scenario with new physics beyond a
certain high-energy cut-off showing up as non-renormalizable operators (NRO) in
the inflaton field. We find that both kinds of models fit remarkably well CMB
and LSS data, with very few free parameters. Besides, a large part of these
models naturally predict a reasonable number of e-folds. A robust feature of
these scenarios is the smallness of tensor perturbations (r < 10^{-3}). The NRO
case can give a sizeable running of the spectral index while achieving a
sufficient number of e-folds. We use Bayesian model comparison tools to assess
the relative performance of the models. We believe that these scenarios can be
considered as a standard physical class of inflationary models, on a similar
footing with monomial potentials.
