# Palatini frames in scalar–tensor theories of gravity

Kozak, Aleksander (Aff1, 0000 0001 1010 5103, grid.8505.8, Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204, Wrocław, Poland) ; Borowiec, Andrzej  (Aff1, 0000 0001 1010 5103, grid.8505.8, Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204, Wrocław, Poland)

13 April 2019

Abstract: A new systematic approach extending the notion of frames to the Palatini scalar–tensor theories of gravity in various dimensions n>2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n>2$\end{document} 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. The formalism provides new frames incorporating non-metricity that lead to re-definition of Jordan frames. The case of Palatini F ( R )-gravity is considered in more detail.

Published in: EPJC 79 (2019) 335 DOI: 10.1140/epjc/s10052-019-6836-y