Non-Gaussian Correlations Outside the Horizon

Abstract

It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial metric divided by the square of the Robertson--Walker scale factor $a$) is time-independent, though with an arbitrary dependence on co-moving coordinates, and all perturbations to the other metric components and to all matter variables vanish, to leading order in $1/a$. The corrections are of order $1/a^2$, and are explicitly given for the reduced metric in a multifield model with a general potential. Further, this is the solution that describes the metric and matter produced by single-field inflation. These results justify the use of observed non-Gaussian correlations (or their absence) as a test of theories of single-field inflation, despite our ignorance of the constituents of the universe while fluctuations are outside the horizon after inflation, as long as graphs with loops can be neglected.

25 pages. This version clarifies the scale transformation used in Section II and the gauge transformation used in Section III, and corrects some typos, including new typos introduced in version 2

References in corpus (19)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Towards the Theory of Reheating After Inflation
• General relativity as an effective field theory: The leading quantum corrections
• Non-Gaussianity from Inflation: Theory and Observations
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Quantum Contributions to Cosmological Correlations
• A new approach to the evolution of cosmological perturbations on large scales
• A general proof of the conservation of the curvature perturbation
• How long before the end of inflation were observable perturbations produced?
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• Primordial non-gaussianities in single field inflation
• Large Non-Gaussianities in Single Field Inflation
• Classical approximation to quantum cosmological correlations
• Non-Gaussianity from Instant and Tachyonic Preheating
• Lattice calculation of non-Gaussianity from preheating
• The CDM isocurvature perturbation in the curvaton scenario
• Very Large Primordial Non-Gaussianity from multi-field: Application to Massless Preheating
• Gradient expansion approach to nonlinear superhorizon perturbations II -- a single scalar field --
• A Tree Theorem for Inflation

Cited by in corpus (30)

• Conformal Symmetries of Adiabatic Modes in Cosmology
• Evolution of fNL to the adiabatic limit
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• Cosmic Microwave Background Observables of Small Field Models of Inflation
• δN formalism
• A parton picture of de Sitter space during slow-roll inflation
• Frame Covariant Nonminimal Multifield Inflation
• Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
• Inflationary perturbation theory is geometrical optics in phase space
• How Gaussian can our Universe be?
• Numerical evaluation of the bispectrum in multiple field inflation
• Non-Gaussianities in Multifield Inflation: Superhorizon Evolution, Adiabaticity, and the Fate of fnl
• Perturbative Reheating After Multiple-Field Inflation: The Impact on Primordial Observables
• The curvature perturbation at second order
• Non-Gaussian Correlations Outside the Horizon II: The General Case
• The δN formula is the dynamical renormalization group
• The structure of correlation functions in single field inflation
• Adiabaticity and the Fate of Non-Gaussianities: The Trispectrum and Beyond
• The scalar bi-spectrum during preheating in single field inflationary models
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Magnetogenesis and the primordial non-gaussianity
• Effect of reheating on predictions following multiple-field inflation
• Probing Compensated Isocurvature with the 21-cm Signal during Cosmic Dawn
• Anisotropic separate universe and Weinberg's adiabatic mode
• Quantum corrections during inflation and conservation of adiabatic perturbations
• Gravity and non-gravity mediated couplings in multiple-field inflation
• Improving Constraints on Inflation with CMB Delensing
• Loops in reheating and cosmological perturbations
• Observable predictions of generalised inflationary scenarios
• Remarks on non-gaussian fluctuations of the inflaton and constancy of ζoutside the horizon