We study the dependence on configuration in momentum space of the primordial 3-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models with higher derivative operators and the DBI model of inflation. We define a cosine between the distributions using a measure based on the ability of experiments to distinguish between them. We find that models fall into two broad categories with fairly orthogonal distributions. Models where non-Gaussianity is created at horizon-crossing during inflation and models in which the evolution outside the horizon dominates. In the first case the 3-point function is largest for equilateral triangles, while in the second the dominant contribution to the signal comes from the influence of long wavelength modes on small wavelength ones. We show that, because the distributions in these two cases are so different, translating constraints on parameters of one model to those of another based on the normalization of the 3-point function for equilateral triangles can be very misleading. rather robust. Although the precise number is model-dependent, in most models |n − 1| is of order 1/N e , where N e is the number of e-folds to the end of inflation when relevant scales exit the horizon. Present limits are of order |n − 1| 0.05 (e.g. [1,2,3]), so that we are entering in the interesting region. A deviation from a flat spectrum would strongly support the slow-roll inflation picture and it would allow to distinguish it from 'ghost inflation' [4] for example, where |n − 1| is expected to be negligible. However, if no tilt is detected slow-roll inflation cannot be safely ruled out: it is easy to build models with a tilt as small as we like.Gravity wave (GW) contribution. The contribution of GWs is directly related to the value of the Hubble constant H during inflation. The detection of a GW signal would therefore point towards models with big vacuum energy (V 1/4 10 16 GeV). Inflationary models fall into two broad categories. Models with small vacuum energy (which is equivalent to a very small ǫ, ǫ ≪ 1/N e , as H/(M P √ ǫ) is fixed by the spectrum normalization) with totally negligible productions of GWs and models with big vacuum energy (usually with ǫ ∼ η ∼ 1/N e ), where the GW contribution should be close to the present experimental limit, r 0.5 (e.g. [1,2]) . The distinction is quite sharp because the two categories can also be distinguished by the variation of the inflaton field during inflation: much smaller than the Planck scale in the first case, comparable to the Planck scale in the second. A possible criticism against models with a sensible production of GWs is that a variation of the inflaton field much bigger than M P seems out of control of the effective field theory [5]. Extra dimensional UV completions provide examples in which this is not true [6]. On the other hand models with very small ǫ have been considered unnatural as they require a hierarchy between the two slow-roll paramet...

After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on higher order statistics of the CMB anisotropies.Since linear evolution preserves the statistical properties of the initial conditions, observed nonGaussianity of the CMB will mirror primordial non-Gaussianity. Single field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of primordial non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianities encoded in the polarization of the CMB. After deriving the optimal weights for a cubic estimator we evaluate the Signal-to-Noise ratio (S/N ) of the estimator for WMAP, Planck and an ideal cosmic variance limited experiment. We find that when the experiment can observe CMB polarization with good sensitivity, the sensitivity to primordial non-Gaussianity increases by roughly a factor of two. We also test the weakly non-Gaussian assumption used to derive the optimal weight factor by calculating the degradation factor produced by the gravitational lensing induced connected four-point function. The physical scales in the radiative transfer functions are largely irrelevant for the constraints on the primordial non-Gaussianity. We show that the total (S/N ) 2 is simply proportional to the number of observed pixels on the sky.

We systematically analyze the primordial non-Gaussianity estimator used by the Wilkinson Microwave Anisotropy Probe (WMAP) science team with the basic ideas of estimation theory in order to see if the limited Cosmic Microwave Background (CMB) data is being optimally utilized. The WMAP estimator is based on the implicit assumption that the CMB bispectrum, the harmonic transform of the three-point correlation function, contains all of the primordial non-Gaussianity information in a CMB map. We first demonstrate that the Signal-to-Noise (S/N ) of an estimator based on CMB three-point correlation functions is significantly larger than the S/N of any estimator based on higher-order correlation functions; justifying our choice to focus on the three-point correlation function. We then conclude that the estimator based on the three-point correlation function, which was used by WMAP, is optimal, meaning it saturates the Cramer-Rao Inequality when the underlying CMB map is nearly Gaussian. We quantify this restriction by demonstrating that the suboptimal character of our estimator is proportonal to the square of the fiducial non-Gaussianity, which is already constrained to be extremely small, so we can consider the WMAP estimator to be optimal in practice. Our conclusions do not depend on the form of the primordial bispectrum, only on the observationally established weak levels of primordial non-Gaussianity.