Direct observations provide constraints on the first two derivatives of the
inflaton potential in slow roll models. We discuss how present day
observations, combined with the flow equations in slow roll parameter space,
provide a non-trivial constraint on the third derivative of the inflaton
potential. We find a lower bound on the third derivative of the inflaton
potential V'''/V > -0.2. We also show that unless the third derivative of the
inflaton potential is unreasonably large, then one predicts the tensor to
scalar ratio, r, to be bounded from below r > 3 * 10^{-6}.Comment: 4 pages, 2 figures. Important sign mistake corrected. Conclusions,
abstract and discussion change
