  We derive some new constraints on single-field inflation from the Wilkinson
Microwave Anisotropy Probe 3-year data combined with the Sloan Luminous Red
Galaxy survey. Our work differs from previous analyses by focusing only on the
observable part of the inflaton potential, or in other words, by making
absolutely no assumption about extrapolation of the potential from its
observable region to its minimum (i.e., about the branch of the potential
responsible for the last ~50 inflationary e-folds). We only assume that
inflation starts at least a few e-folds before the observable Universe leaves
the Hubble radius, and that the inflaton rolls down a monotonic and regular
potential, with no sharp features or phase transitions. We Taylor-expand the
inflaton potential at order v=2, 3 or 4 in the vicinity of the pivot scale,
compute the primordial spectra of scalar and tensor perturbations numerically
and fit the data. For v>2, a large fraction of the allowed models is found to
produce a large negative running of the scalar tilt, and to fall in a region of
parameter space where the second-order slow-roll formalism is strongly
inaccurate. We release a code for the computation of inflationary perturbations
which is compatible with CosmoMC.
