Theology, News and Notes - Vol. 36, No. 02

Theology News & Notes was a theological journal published by Fuller Theological Seminary from 1954 through 2014.https://digitalcommons.fuller.edu/tnn/1103/thumbnail.jp

Transport equations for the inflationary trispectrum

We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.Comment: 24 pages, plus references and appendix. v2: matches version published in JCAP; typo fixed in Eq. (54

General analytic predictions of two-field inflation and perturbative reheating

16 pages, 5 figures, Version 2 includes a revised comparison with Meyers and Tarrant [41

Optimal bispectrum constraints on single-field models of inflation

We use WMAP 9-year bispectrum data to constrain the free parameters of an 'effective field theory' describing fluctuations in single-field inflation. The Lagrangian of the theory contains a finite number of operators associated with unknown mass scales. Each operator produces a fixed bispectrum shape, which we decompose into partial waves in order to construct a likelihood function. Based on this likelihood we are able to constrain four linearly independent combinations of the mass scales. As an example of our framework we specialize our results to the case of 'Dirac-Born-Infeld' and 'ghost' inflation and obtain the posterior probability for each model, which in Bayesian schemes is a useful tool for model comparison. Our results suggest that DBI-like models with two or more free parameters are disfavoured by the data by comparison with single parameter models in the same class

The δN formula is the dynamical renormalization group

We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.Comment: v1: 33 pages, plus appendix and references; 5 figures. v2: typographical typos fixed, minor changes to the main text and abstract, reference added; matches version published in JCA

The inflationary bispectrum with curved field-space

We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.Comment: 22 pages, plus appendix and reference