Further Extended Theories of Gravitation: Part II

TL;DR

This paper explores advanced theories of gravity in the Palatini formalism, demonstrating their complexity beyond simple f(R) models and showing how they can produce non-trivial Weyl geometries with matter coupling.

Contribution

It introduces specific extended gravity models in the Palatini formalism with matter, illustrating their distinct features from standard f(R) theories and their ability to generate non-trivial Weyl geometries.

Findings

Extended theories do not trivially reduce to f(R) models.

Examples of theories producing non-trivial Weyl geometries.

Matter coupling affects the geometric structure of spacetime.

Abstract

We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in ref. [1] does not trivially reduce to f(R) models. It will also produce an example of theory that on-shell endowes spacetime with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers-Pirani-Schild; see ref. [2]).