Gravity and non-gravity mediated couplings in multiple-field inflation

Mechanisms for the generation of primordial non-Gaussian metric fluctuations in the context of multiple-field inflation are reviewed. As long as kinetic terms remain canonical, it appears that nonlinear couplings inducing non-gaussianities can be split into two types. The extension of the one-field results to multiple degrees of freedom leads to gravity mediated couplings that are ubiquitous but generally modest. Multiple-field inflation offers however the possibility of generating non-gravity mediated coupling in isocurvature directions that can eventually induce large non-Gaussianities in the metric fluctuations. The robustness of the predictions of such models is eventually examined in view of a case study derived from a high-energy physics construction.Comment: 14 pages, 3 figures, invited review for CQG issue on non-linear cosmolog

Scale dependence of fNLf_{NL} in N-flation

Adopting the horizon-crossing approximation, we derive the spectral index of $f_{NL}$ in general N-flation model. Axion N-flation model is taken as a typical model for generating a large $f_{NL}$ which characterizes the size of local form bispectrum. We find that its tilt $n_{f_{NL}}$ is negligibly small when all inflatons have the same potential, but a negative detectable $n_{f_{NL}}$ can be achieved in the axion N-flation with different decay constants for different inflatons. The measurement of $n_{f_{NL}}$ can be used to support or falsify the axion N-flation in the near future.Comment: 15 pages, 2 figures; a subsection with detectable scale dependence of f_NL added; more discussions added and version accepted for publication in JCA

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.Comment: Accepted to JCAP. 22 pages, 4 figure

Inhomogeneous non-Gaussianity

We propose a method to probe higher-order correlators of the primordial density field through the inhomogeneity of local non-Gaussian parameters, such as f_NL, measured within smaller patches of the sky. Correlators between n-point functions measured in one patch of the sky and k-point functions measured in another patch depend upon the (n+k)-point functions over the entire sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to detect or constrain higher-order correlators in local models of non-Gaussianity, as well as to distinguish between single and multiple-source scenarios for generating the primordial density perturbation, and more generally to probe the details of inflationary physics.Comment: 16 pages, 2 figures; v2: Minor changes and references added. Matches the published versio

CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and \tau_{NL}) and a New Consistency Test of Single-Field Inflation

We outline the expected constraints on non-Gaussianity from the cosmic microwave background (CMB) with current and future experiments, focusing on both the third (f_{NL}) and fourth-order (g_{NL} and \tau_{NL}) amplitudes of the local configuration or non-Gaussianity. The experimental focus is the skewness (two-to-one) and kurtosis (two-to-two and three-to-one) power spectra from weighted maps. In adition to a measurement of \tau_{NL} and g_{NL} with WMAP 5-year data, our study provides the first forecasts for future constraints on g_{NL}. We describe how these statistics can be corrected for the mask and cut-sky through a window function, bypassing the need to compute linear terms that were introduced for the previous-generation non-Gaussianity statistics, such as the skewness estimator. We discus the ratio A_{NL} = \tau_{NL}/(6f_{NL}/5)^2 as an additional test of single-field inflationary models and discuss the physical significance of each statistic. Using these estimators with WMAP 5-Year V+W-band data out to l_{max}=600 we constrain the cubic order non-Gaussianity parameters \tau_{NL}, and g_{NL} and find -7.4 < g_{NL}/10^5 < 8.2 and -0.6 < \tau_{NL}/10^4 < 3.3 improving the previous COBE-based limit on \tau_{NL} < 10^8 nearly four orders of magnitude with WMAP.Comment: 15 pages. 14 figure

Local non-Gaussianity from inflation

The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.Comment: 21 pages, 1 figure, invited review to appear in Classical and Quantum Gravity special issue on non-linear and non-Gaussian cosmological perturbation

Scale-dependent non-Gaussianity probes inflationary physics

We calculate the scale dependence of the bispectrum and trispectrum in (quasi) local models of non-Gaussian primordial density perturbations, and characterize this scale dependence in terms of new observable parameters. They can help to discriminate between models of inflation, since they are sensitive to properties of the inflationary physics that are not probed by the standard observables. We find consistency relations between these parameters in certain classes of models. We apply our results to a scenario of modulated reheating, showing that the scale dependence of non-Gaussianity can be significant. We also discuss the scale dependence of the bispectrum and trispectrum, in cases where one varies the shape as well as the overall scale of the figure under consideration. We conclude providing a formulation of the curvature perturbation in real space, which generalises the standard local form by dropping the assumption that f_NL and g_NL are constants.Comment: 27 pages, 2 figures. v2: Minor changes to match the published versio

On the divergences of inflationary superhorizon perturbations

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $\Delta N$ formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.Comment: 12 page