A class of ghost-free theories in symmetric teleparallel geometry

TL;DR

This paper introduces a new class of ghost-free theories within symmetric teleparallel geometry, leveraging Transverse Diffeomorphism symmetry to avoid instabilities common in similar frameworks.

Contribution

The work constructs and demonstrates a class of ghost-free symmetric teleparallel theories, connecting them to scalar-tensor models and Horndeski theories, with implications for matter coupling.

Findings

Theories are free of ghost-like instabilities.

Explicit equivalence to scalar-tensor models established.

Compatibility with Horndeski theories and matter couplings shown.

Abstract

Theories formulated in the arena of teleparallel geometries are generically plagued by ghost-like instabilities or other pathologies that are ultimately caused by the breaking of some symmetries. In this work, we construct a class of ghost-free theories based on a symmetry under Transverse Diffeomorphisms that is naturally realised in symmetric teleparallelism. We explicitly show their equivalence to a family of theories with an extra scalar field plus a global degree of freedom and how Horndeski theories and healthy couplings to matter fields can be readily accommodated.