Jordan frame beyond scalar-tensor theories

Understand

We study the Jordan frame formulation of generalizations of scalar-tensor theories conceived by replacing the scalar with other fields such as vectors.

• The generic theory in this family contains higher order time derivative terms in the Jordan frame action which is indicative of ill-posedness.
• However, we show that equations of motion can always be reduced to a second-order-in-time form as long as the original Einstein frame formulation is well posed.
• The inverse transformation from the Jordan frame back to the Einstein frame is not possible for all field values in all theories, but we obtain a fully invertible transformation for vector-tensor theories by a redefinition of the vector field.