Constraining Running Non-Gaussianity

TL;DR

The paper develops a Fisher-matrix framework to constrain scale-dependent primordial non-Gaussianity, focusing on a running parameter n_{NG} paired with the amplitude f_{NL} for local and equilateral shapes. It analyzes CMB bispectrum data (temperature and polarization) and extends forecasts to large-scale structure via galaxy power spectra and bispectra, highlighting complementarity between probes. The authors apply the method to DBI inflation as a case study, showing how constraints on f_{NL}(k) translate into limits on DBI parameters, and conclude that future CMB and LSS surveys together can robustly test running non-Gaussianity and differentiate inflationary scenarios. Overall, the work emphasizes the value of jointly exploiting CMB and LSS data to uncover scale-dependent primordial signatures with substantial implications for early-universe physics.

Abstract

The primordial non-Gaussian parameter fNL has been shown to be scale-dependent in several models of inflation with a variable speed of sound. 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 nNG that quantifies the running of fNL(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 fNL = 50 for the local model and fNL = 100 for the equilateral model of non-Gaussianity, is able to determine nNG with a 1-sigma uncertainty of Delta nNG = 0.1 and Delta nNG = 0.3, respectively, for the Planck mission. In addition, we consider a Fisher matrix analysis of the galaxy power spectrum to determine the expected constraints on the running parameter nNG for the local model and of the galaxy bispectrum for the equilateral model from future 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 fNL(k) translate into constraints on the parameter space of the theory.

Figures (14)

• Figure 1: Local model. 1-$\sigma$ constraints on $f_{\rm NL}$ and $n_{\rm NG}$ assuming $k_p=0.04$ Mpc$^{-1}$ and fiducial values $f_{\rm NL}=50$, $n_{\rm NG}=0$. Dashed lines correspond to the limits from the temperature information alone, dotted lines to polarization (EEE), while the continuous lines correspond to all bispectrum combinations. We consider WMAP ( upper left panel), Planck ( upper right), CMBPol ( bottom left) and an ideal CMB experiment ( bottom right).
• Figure 2: Local model. Expected marginalized ( thick, blue lines) and unmarginalized ( thin, red lines) errors for $f_{\rm NL}$ ( left panels) and $n_{\rm NG}$ ( right panels) as a function of $l_{max}$ for Planck ( central panel) and CMBPol ( lower panels).
• Figure 3: Equilateral model. 1-$\sigma$ constraints on $f_{\rm NL}$ and $n_{\rm NG}$ assuming $k_p=0.04$ Mpc$^{-1}$ and fiducial values $f_{\rm NL}=100$, $n_{\rm NG}=0$. Dashed lines correspond to the limits from the temperature information alone, dotted lines to polarization (EEE), while the continuous lines correspond to all bispectrum combinations. We consider WMAP ( upper left panel), Planck ( upper right), CMBPol ( bottom left) and an ideal CMB experiment ( bottom right).
• Figure 4: Equilateral model. Expected marginalized ( thick, blue lines) and unmarginalized ( thin, red lines) errors for $f_{\rm NL}$ ( left panels) and $n_{\rm NG}$ ( right panels) as a function of $l_{max}$ for Planck ( central panel) and CMBPol ( lower panels).
• Figure 5: $1-\sigma$ contours for CMBPol assuming different fiducial values for the parameters. Left panel: local model for $f_{\rm NL}=5, 25, 50$. Right panel: equilateral model for $f_{\rm NL}=10, 50, 100$. In both cases we also consider $n_{\rm NG}=0$ ( continuous, red lines), $0.1$ ( dashed, blue lines) and $-0.1$ ( dotted, green lines).