Observational constraints on the inflaton potential combined with flow equations in inflaton space

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 x 10(-6).