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Inflationary perturbation theory is geometrical optics in phase space
journal contribution
posted on 2023-06-08, 12:21 authored by David SeeryDavid Seery, David Mulryne, Jonathan Frazer, Raquel RibeiroA 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 "dN" 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, ?, 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.
History
Publication status
- Published
Journal
Journal of Cosmology and Astroparticle PhysicsISSN
1475-7516Publisher
Institute of PhysicsExternal DOI
Issue
9Volume
2012Page range
010Department affiliated with
- Physics and Astronomy Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-09-25First Compliant Deposit (FCD) Date
2012-09-07Usage metrics
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