Abstract
The existence of a consistent bimetric theory raises an intriguing question: which is the physical metric? In Chaps. 3 and 4 we chose to couple only one of the two metric, \(g_{\mu \textit{v}}\), directly to matter, while the other dynamical metric, \(f_{\mu \textit{v}}\), only interacts with matter fields indirectly through its interactions with \(g_{\mu \nu }\).
O, that way madness lies; let me shun that;
No more of that.
Lear, King Lear, 3.4
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Notes
- 1.
Using the same principles, further candidate double couplings have been constructed in Ref. [11], but it is not yet known which, if any, of these are ghost-free.
- 2.
- 3.
This will be the case in particular if \(g_{\mu \textit{v}}\) and \(f_{\mu \textit{v}}\) are conformally related, as then a lightlike path in one metric is also lightlike in the other.
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Solomon, A.R. (2017). The Geometry of Doubly-Coupled Bigravity. In: Cosmology Beyond Einstein. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-46621-7_5
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