Auxiliary fields representation for modified gravity models

TL;DR

This paper develops tensor-multiscalar representations for various modified gravity models, simplifying their analysis by introducing auxiliary fields and exploring conditions for cosmological solutions.

Contribution

It presents a systematic procedure to reformulate complex modified gravity actions into equivalent scalar-tensor theories with auxiliary fields, including new insights into cosmological constant calibration.

Findings

Equivalent scalar-tensor formulations for complex gravity actions

Conditions for de Sitter solutions in modified gravity models

Reduction of auxiliary fields in specific models

Abstract

We consider tensor-multiscalar representations for several types of modified gravity actions. The first example is the theory with the action representing an arbitrary smooth function of the scalar curvature R and (Box R), the integrand of the Gauss-Bonnet term and the square of the Weyl tensor. We present a simple procedure leading to an equivalent theory of a space-time metric and four auxiliary scalars and specially discuss calibration of a cosmological constant and the condition of the existence of dS-like solutions in the case of empty universe. The condition for obtaining a smaller number of independent scalar fields is derived. The second example is the Eddington-like gravity action. In this case we show, in particular, the equivalence of the theory to GR with the cosmological constant term, with or without use of the first-order formalism, and also discuss some possible generalizations.