Moment transport equations for the primordial curvature perturbation

Mulryne, David J, Seery, David and Wesley, Daniel (2011) Moment transport equations for the primordial curvature perturbation. Journal of Cosmology and Astroparticle Physics, 2011 (04). 030.

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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.

Item Type: Article
Additional Information: Author list in alphabetical order.
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Depositing User: David Seery
Date Deposited: 06 Feb 2012 20:27
Last Modified: 02 Apr 2012 08:55
URI: http://sro.sussex.ac.uk/id/eprint/25994
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