Constraining running non-gaussianity

The primordial non-Gaussian parameter f(NL) has been shown to be scale-dependent in several models of inflation with a variable speed of sound, such as Dirac-Born-Infeld (DBI) models. We perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter n(NG) that quantifies the running of f(NL)(k) for current and future CMB missions. We find that CMB information alone, in the event of a significant detection of the non-Gaussian component, corresponding to f(NL) = 50 for the local model and f(NL) = 100 for the equilateral model of non-Gaussianity, is able to determine n(NG) with a 1-sigma uncertainty of Delta n(NG) similar or equal to 0.1 and Delta n(NG) similar or equal to 0.3, respectively, for the Planck mission and a factor of two better for CMBPol. In addition, we show how future large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the non-Gaussian signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent f(NL) (k) translate into constraints on the parameter space of the theory.