Multi-Scalar-Tensor Equivalents for Modified Gravitational Actions

TL;DR

This paper develops a general framework for deriving scalar-tensor equivalents of modified gravity actions using differential forms and first order formalism, applicable to various gravitational models including cosmologically relevant ones.

Contribution

It introduces a systematic method to construct scalar-tensor equivalents for a wide class of modified gravitational actions, including Riemannian and non-Riemannian cases.

Findings

Explicit scalar-tensor equivalents for $f(R)$ models.

Scalar-tensor forms for quadratic curvature Lagrangians.

Application to models involving gradients of scalar curvature.

Abstract

A general scheme of constructing scalar-tensor equivalents to modified gravitational actions are studied using the algebra of exterior differential forms and the first order formalism that allows an independent connection and coframe. By introducing appropriate constraints on the connection, pseudo-Riemannian cases as well as non-Riemannian cases are discussed for various gravitational models. The issue of the dynamical degree of freedom for the resulting scalar fields is discussed at the level of the field equations. Explicit scalar-tensor equivalents for gravitational models based on $f(R)$ models, the quadratic curvature lagrangians and the models involving the gradients of the scalar curvature are presented. In particular, explicit ST equivalence for gravitational lagrangians popular in some cosmological models are constructed.