Disformal Transformations in Scalar–Torsion Gravity

Manuel Hohmann

doi:10.3390/universe5070167

Abstract

We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar–torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories.

Highlights

Scalar–tensor models form one of the largest and most well-studied classes of gravitational theories. While this term most often refers to scalar-curvature theories [1], which can be regarded as scalar extensions of general relativity based on its standard formulation in terms of curvature, it can appropriately be applied to scalar field extensions of teleparallel gravity based on torsion [2,3,4,5] or symmetric teleparallel gravity based on non-metricity [6,7], and to scalar extensions of each of the three geometric pictures of gravity [8]
We aim to construct a class of scalar–torsion theories of gravity which is closed under disformal transformations, and from which teleparallel analogues of Horndeski and beyond Horndeski models may be derived
We have discussed disformal transformations in the context of scalar–torsion extensions of teleparallel gravity and derived the transformation behavior of the most important geometric quantities used in these theories

Summary

Introduction

Scalar–tensor models form one of the largest and most well-studied classes of gravitational theories. Levi–Civita connection, this leads to the well-known possibility of conformal transformations [10], or the more general class of disformal transformations [11,12] and its extensions [13,14] The latter are of particular interest, as they connect classes of gravity theories with second order field equations, such as the well-known Horndeski class [15,16,17], to such higher derivative order theories which are healthy in the sense that they avoid Ostrogradsky instabilities due to the presence of constraints arising from degeneracies in their Lagrangians [18,19,20,21].

Geometric Notions

Disformal Transformations

A Disformally Invariant Class of Theories

The Quadratic Class of Actions

H I1 I2 a1 a2

Conclusions