Equivalence of cosmological observables in conformally related scalar tensor theories

Rondeau, François; Li, Baojiu

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).

Citation

Rondeau, F., & Li, B. (2017). Equivalence of cosmological observables in conformally related scalar tensor theories. Physical Review D, 96(12), Article 124009. https://doi.org/10.1103/physrevd.96.124009

• 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