Constraining running non-gaussianity

Abstract

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. Starting from a simple ansatz for a scale-dependent amplitude of the primordial curvature bispectrum for two common phenomenological models of primordial non-Gaussianity, 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 such as WMAP, Planck and CMBPol. 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-σ uncertainty of ∆n NG 0.1 and ∆n NG 0.3, respectively, for the Planck mission and a factor of two better for CMBPol. In addition, we consider a simple Fisher matrix analysis of the galaxy power spectrum to determine the expected constraints on the running parameter n NG for the local model and of the galaxy bispectrum for the equilateral model from future planned and proposed photometric and spectroscopic surveys. We find that, in both cases, 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.

Inflation and String Theory

“…On smaller scales, a significant evolution of the spectrum and hence of the sound speed is still allowed. Large-scale structure constraints on the running of the spectrum were analyzed in [721].…”

Influence of reheating on the trispectrum and its scale dependence

“…By measurements of the CMB µ-distortion in a CMB experiment such as PIXIE, f NL and n τNL could also be measured to an accurancy of the order of O(0.3) and O(0.6) respectively for f NL = 20 and τ NL = 5000, and similarly in large-scale surveys such as Euclid [48]. 1 For any non-linearity parameter, the error bar on its scale dependence is approximately inversely proportional to its fiducial value [47].…”

Oscillations in the primordial bispectrum: Mode expansion

“…This direction is set by the direction in which k i picks up a minus sign due to the Bunch Davies vacuum perturbation as explained in [24]. One could allow for scale invariance breaking and consider BEFT, however there are some suggestions [36] that such large scale invariance should have been observed already. We can rewrite the bispec- (9) is set to k * = 0.002Mpc −1 and x1 = 1 → k1 = kmax.…”