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Equivalence of cosmological observables in conformally related scalar tensor theories.

Rondeau, François and Li, Baojiu (2017) 'Equivalence of cosmological observables in conformally related scalar tensor theories.', Physical review D., 96 (12). p. 124009.


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).

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Publisher 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.
Date accepted:29 September 2017
Date deposited:05 January 2018
Date of first online publication:12 December 2017
Date first made open access:05 January 2018

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