Gravity with Auxiliary Fields

TL;DR

This paper investigates modifications to General Relativity involving nondynamical auxiliary fields, revealing that such theories generally entail higher-order derivatives of matter fields and can be characterized by just two parameters at next-to-leading order.

Contribution

It introduces a covariant framework for modified gravity with nondynamical fields, deriving a minimal parametrization and demonstrating how to constrain these theories independently of specific models.

Findings

Higher-order derivatives of matter fields are generically present in these theories.

A two-parameter description suffices at next-to-leading order.

The approach enables theory-independent constraints, exemplified in the Newtonian limit.

Abstract

Modifications of General Relativity usually include extra dynamical degrees of freedom, which to date remain undetected. Here we explore the possibility of modifying Einstein's theory by adding solely nondynamical fields. With the minimal requirement that the theory satisfies the weak equivalence principle and admits a covariant Lagrangian formulation, we show that the field equations generically have to include higher-order derivatives of the matter fields. This has profound consequences for the viability of these theories. We develop a parametrization based on a derivative expansion and show that - to next to leading order - all theories are described by just two parameters. Our approach can be used to put stringent, theory-independent constraints on such theories, as we demonstrates using the Newtonian limit as an example.