First Constraints on the Running of Non-Gaussianity

We use data from the Wilkinson Microwave Anisotropy probe temperature maps to constrain a scale-dependent generalization of the popular "local'' model for primordial non-Gaussianity. In the model where the parameter f(NL) is allowed to run with scale k, f(NL)(k) = f(NL)*(k/k(piv))(nfNL), we constrain the running to be n(fNL) = 0.30(-1.2)(+1.9) at 95% confidence, marginalized over the amplitude f(NL)*. The constraints depend somewhat on the prior probabilities assigned to the two parameters. In the near future, constraints from a combination of Planck and large-scale structure surveys are expected to improve this limit by about an order of magnitude and usefully constrain classes of inflationary models.