Inflationary perturbation theory is geometrical optics in phase space

Abstract

A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Taylor expansion. Our method produces ordinary differential equations which allow the Taylor coefficients to be computed efficiently. We use raytracing methods to express the gauge transformation between field fluctuations and the curvature perturbation, zeta, in geometrical terms. Using these results we give a compact expression for the nonlinear gauge-transform part of fNL in terms of the principal curvatures of uniform energy-density hypersurfaces in field space.

22 pages, plus bibliography and appendix. v2: minor changes, matches version published in JCAP

References in corpus (13)

• Non-Gaussianities in two-field inflation
• Inflation after WMAP3: Confronting the Slow-Roll and Exact Power Spectra with CMB Data
• Curvature and isocurvature perturbations in two-field inflation
• CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Non-gaussianity and cosmic uncertainty in curvaton-type models
• Nflation: multi-field inflationary dynamics and perturbations
• de Sitter limit of inflation and nonlinear perturbation theory
• Classicality of the primordial perturbations
• Moment transport equations for the primordial curvature perturbation
• Non-Gaussian Correlations Outside the Horizon
• Non-Gaussianities in Multifield Inflation: Superhorizon Evolution, Adiabaticity, and the Fate of fnl
• Numerical calculation of second order perturbations

Cited by in corpus (11)

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• Numerical evaluation of the bispectrum in multiple field inflation
• Hybrid Inflation in the Complex Plane
• MultiModeCode: An efficient numerical solver for multifield inflation
• On reaching the adiabatic limit in multi-field inflation
• Transport equations for the inflationary trispectrum
• Effect of reheating on predictions following multiple-field inflation
• Round table on Standard Model Anomalies
• Non-Gaussianity in D3-brane inflation
• Non-Gaussianity after many-field reheating