Slow Roll Reconstruction: Constraints on Inflation from the 3 Year WMAP Dataset

We study the constraints on the inflationary parameter space derived from the 3 year WMAP dataset using ``slow roll reconstruction'', using the SDSS galaxy power spectrum to gain further leverage where appropriate. This approach inserts the inflationary slow roll parameters directly into a Monte Carlo Markov chain estimate of the cosmological parameters, and uses the inflationary flow hierarchy to compute the parameters' scale-dependence. We work with the first three parameters (epsilon, eta and xi) and pay close attention to the possibility that the 3 year WMAP dataset contains evidence for a ``running'' spectral index, which is dominated by the xi term. Mirroring the WMAP team's analysis we find that the permitted distribution of xi is broad, and centered away from zero. However, when we require that inflationary parameters yield at least 30 additional e-folds of inflation after the largest observable scales leave the horizon, the bounds on xi tighten dramatically. We make use of the absence of an explicit pivot scale in the slow roll reconstruction formalism to determine the dependence of the computed parameter distributions on the pivot. We show that the choice of pivot has a significant effect on the inferred constraints on the inflationary variables, and the spectral index and running derived from them. Finally, we argue that the next round of cosmological data can be expected to place very stringent constraints on the region of parameter space open to single field models of slow roll inflation.Comment: 26 pages, 11 figures, JHEP format. v2: version accepted by JCAP: minor clarifications and references added, 1 figure added, v3: 1 reference adde

Large Non-Gaussianities in Single Field Inflation

We compute the 3-point correlation function for a general model of inflation driven by a single, minimally coupled scalar field. Our approach is based on the numerical evaluation of both the perturbation equations and the integrals which contribute to the 3-point function. Consequently, we can analyze models where the potential has a "feature", in the vicinity of which the slow roll parameters may take on large, transient values. This introduces both scale and shape dependent non-Gaussianities into the primordial perturbations. As an example of our methodology, we examine the ``step'' potentials which have been invoked to improve the fit to the glitch in the $$ $C_l$ for $l \sim 30$, present in both the one and three year WMAP data sets. We show that for the typical parameter values, the non-Gaussianities associated with the step are far larger than those in standard slow roll inflation, and may even be within reach of a next generation CMB experiment such as Planck. More generally, we use this example to explain that while adding features to potential can improve the fit to the 2-point function, these are generically associated with a greatly enhanced signal at the 3-point level. Moreover, this 3-point signal will have a very nontrivial shape and scale dependence, which is correlated with the form of the 2-point function, and may thus lead to a consistency check on the models of inflation with non-smooth potentials.Comment: 23 pages JHEP-style, 7 Figures. Updated with improved results. Accepted for publication by JCA