Scalar-multitensor approach to teleparallel modified theories of gravity

Abstract

The analysis of teleparallel $f(T,{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{1}}T,\dots{},{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{n}}\ensuremath{\cdots}{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{1}}T)$ gravity in the Jordan and Einstein frames is presented. The equivalence between $f(T,{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{1}}T,\dots{},{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{n}}\ensuremath{\cdots}{\ensuremath{\nabla}}_{{\ensuremath{\mu}}_{1}}T)$ gravity and a scalar-multitensor theory is proved in both frames for systems with a regular Hessian matrix. For each order of derivative an auxiliary tensor of the same order is introduced. As a consequence, the order of the differential equation for the tetrad field is reduced to an equation of order two, but the price to be paid is the analysis of a system of coupled equations for the auxiliary fields.