From higher dimensional theories, e.g. string theory, one expects the presence of nonminimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a classical …

We study metric transformations which depend on a scalar field and its first derivatives and confirm that the number of physical degrees of freedom does not change under such transformations, as long as they are not singular. We perform a Hamiltonian …

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open …

Physical equivalence between different conformal frames in scalar-tensor theory of gravity is a known fact. However, assuming that matter minimally couples to the metric of a particular frame, which we call the matter Jordan frame, the matter point …

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