First constraints on the running of non-Gaussianity

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.

Scale-Dependent Non-Gaussianity as a Generalization of the Local Model

We generalize the local model of primordial non-Gaussianity by promoting the parameter fNL to a general scale-dependent function fNL(k). We calculate the resulting bispectrum and the effect on the bias of dark matter halos, and thus the extent to which fNL(k) can be measured from the large-scale structure observations. By calculating the principal components of fNL(k), we identify scales where this form of non-Gaussianity is best constrained and estimate the overlap with previously studied local and equilateral non-Gaussian models.