Palatini frames in scalar-tensor theories of gravity

TL;DR

This paper develops a systematic approach to analyze Palatini scalar-tensor theories of gravity, introducing invariant frames and characteristics, and explores their implications, especially in four dimensions and for F(R)-gravity.

Contribution

It extends the notion of frames to Palatini theories, characterizes invariant subclasses, and introduces new frames including non-metricity effects.

Findings

Dimension four has a unique transformation group structure.

Invariant characteristics effectively classify solution-equivalent theories.

New frames incorporating non-metricity are constructed.

Abstract

A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal transformations. We characterize theories invariant with respect to these transformations dividing them up into solution-equivalent subclasses (group orbits). To this end, invariant characteristics have been introduced. Unlike in the metric case, it turns out that the dimension four admitting the largest transformation group is rather special for such theories. The formalism provides new frames that incorporate non-metricity. The case of Palatini F(R)-gravity is considered in more detail.