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)^n_fNL, 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.