Conformal and kinetic couplings as two Jordan frames of the same theory

Abstract

Certain scalar-tensor (ST) theories with non-minimal coupling of the scalar field to curvature may admit an Einstein frame representation, where gravity is described by the Einstein–Hilbert action plus the scalar sector. Between them, some theories exactly coincide in their respective Einstein frames. If transformations between Jordan and Einstein frames are invertible, these theories can be associated with two Jordan frames of the unique theory. Such successive dualities can connect theories with non-derivative coupling, like $$R\phi ^2$$Rϕ2, with derivatively coupled theories, like Horndeski and DHOST. In absence of matter, these are equivalent, though looking very different. We show the existence of a successive duality between the $$R\phi ^2$$Rϕ2 theory and a recently found Palatini kinetically coupled theory, which both look in their Einstein frames as Einstein theory minimally coupled to scalar. Transforming singular exact solutions of the latter to Jordan frames, we compare desingularization properties of the above two theories which both violate the null energy condition. It is found that kinetically coupled theory has stronger desingularization features, exhibiting possibility of Genesis-type behavior of the homogeneous and isotropic cosmological solutions.

Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation

“…1 Higgs inflation, where the field couples directly to the Ricci scalar has been much studied in the Palatini formulation, and the predictions are different than in the metric case . Inflation in the case when derivatives of the field couple directly to the curvature has also been studied [91][92][93][94]; in [95], such a theory was used for quintessence (see also [96][97][98][99]). Unlike in the case when only the field couples directly to the curvature, in the derivative coupling case the results of the metric and the Palatini formulation are close to each other.…”