Aleksander Kozak

Palatini frames in scalar-tensor theories

Conformal transformations play an important role in the scalar-tensor theories of gravity, as they allow one to carry out calculations in a more convenient frame, simplifying the field equations. In the Palatini approach, however, the metric structure of space-time is decoupled from its affine structure, so that a transformation of the metric tensor does not entail a corresponding change in the linear connection. One needs to define independent transformation for the connection, reducing to the standard formula in case the connection is Levi-Civita with respect to the metric. In my presentation, I shall present a scalar-tensor theory taking into account such transformation, called 'generalized almost-geodesic mapping', and discuss properties of the solution to the field equation for the connection. The theory will be analysed in both the Einstein and the Jordan frame. I will also introduce invariant quantities, whose functional form remains unchanged irrespective of the conformal frame, and show how they can be applied to analysis of possible equivalence between F(R) and scalar-tensor theories of gravity in the Palatini formalism.