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Equivalence of cosmological observables in conformally related scalar tensor theories

Rondeau, François; Li, Baojiu

Equivalence of cosmological observables in conformally related scalar tensor theories Thumbnail


Authors

François Rondeau



Abstract

Scalar tensor theories can be expressed in different frames, such as the commonly used Einstein and Jordan frames, and it is generally accepted that cosmological observables are the same in these frames. We revisit this by making a detailed side-by-side comparison of the quantities and equations in two conformally related frames, from the actions and fully covariant field equations to the linearized equations in both real and Fourier spaces. This confirms that the field and conservation equations are equivalent in the two frames, in the sense that we can always re-express equations in one frame using relevant transformations of variables to derive the corresponding equations in the other. We show, with both analytical derivation and a numerical example, that the line-of-sight integration to calculate CMB temperature anisotropies can be done using either Einstein frame or Jordan frame quantities, and the results are identical, provided the correct redshift is used in the Einstein frame (1 þ z ≠ 1=a).

Journal Article Type Article
Acceptance Date Sep 29, 2017
Online Publication Date Dec 12, 2017
Publication Date Dec 12, 2017
Deposit Date Jan 5, 2018
Publicly Available Date Jan 5, 2018
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 12
Article Number 124009
DOI https://doi.org/10.1103/physrevd.96.124009
Public URL https://durham-repository.worktribe.com/output/1337300

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Copyright Statement
Reprinted with permission from the American Physical Society: Rondeau, François & Li, Baojiu (2017). Equivalence of cosmological observables in conformally related scalar tensor theories. Physical Review D 96(12): 124009 © 2017 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.






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