Moment transport equations for the primordial curvature perturbation

Abstract

In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of zeta on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, fNL. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of fNL. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M^3). The performance of the moment transport algorithm means that numerical calculations with M >> 1 fields are straightforward. We illustrate this performance with a numerical calculation of fNL in Nflation models containing M ~ 10^2 fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as gNL.

23 pages, plus appendices and references; 4 figures. v2: incorrect statements regarding numerical delta N removed from Sec. 4.3. Minor modifications elsewhere

References in corpus (7)

• Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
• Non-Gaussianities in two-field inflation
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Nflation: multi-field inflationary dynamics and perturbations
• Nflation: non-gaussianity in the horizon-crossing approximation
• Primordial non-Gaussianity in the large scale structure of the Universe
• A Study of High-Order Non-Gaussianity with Applications to Massive Clusters and Large Voids

Cited by in corpus (10)

• Inflationary perturbation theory is geometrical optics in phase space
• Numerical evaluation of the bispectrum in multiple field inflation
• MultiModeCode: An efficient numerical solver for multifield inflation
• Primordial black holes and gravitational waves from nonminimally coupled supergravity inflation
• Reheating, Multifield Inflation and the Fate of the Primordial Observables
• Transport equations for the inflationary trispectrum
• Separable and non-separable multi-field inflation and large non-Gaussianity
• Inflation, SUSY breaking, and primordial black holes in modified supergravity coupled to chiral matter
• Effective dynamics of quantum fluctuations in field theory: with applications to cosmology
• Non-Gaussianity in D3-brane inflation