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Adiabatic and isocurvature perturbation projections in multi-field inflation

Gordon, Chris; Saffin, Paul M.

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Chris Gordon

Professor of Physics


Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the isocurvature perturbation in the flat field space limit.


Gordon, C., & Saffin, P. M. (2013). Adiabatic and isocurvature perturbation projections in multi-field inflation. Journal of Cosmology and Astroparticle Physics, 2013(8), Article 021.

Journal Article Type Article
Acceptance Date Jul 9, 2013
Publication Date Aug 12, 2013
Deposit Date Apr 24, 2017
Publicly Available Date Apr 24, 2017
Journal Journal of Cosmology and Astroparticle Physics
Electronic ISSN 1475-7516
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 2013
Issue 8
Article Number 021
Keywords Inflation, Cosmological perturbation theory
Public URL
Publisher URL
Additional Information This is an author-created, un-copyedited version of an article accepted for publication/published
in Journal of Cosmology and Astroparticle Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at


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