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Disformal transformations of Friedmann-Lema\^tre-Robertson-Walker and Bianchi geometries are analyzed in the context of scalar-tensor gravity. Novel aspects discussed explicitly are the 3+1 splitting, the effective fluid equivalent of the gravitational scalar, Bianchi models, stealth solutions, and de Sitter solutions with nonconstant scalar field (which are signatures of scalar-tensor gravity). Both pure disformal transformations and more general ones are discussed, including those containing higher derivatives of the scalar field recently introduced in the literature.
Faraoni et al. (Mon,) studied this question.