  We use data from the WMAP temperature maps to constrain a scale-dependent
generalization of the popular 'local' model for primordial non-Gaussianity. In
the model where the parameter fNL is allowed to run with scale k, fNL(k) = fNL*
(k/k_piv)^n, we constrain the running to be n = 0.30(+1.9)(-1.2) at 95%
confidence, marginalized over the amplitude fNL*. 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.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory