Scalar-multi-tensor approach to fT,B,∇μT,∇μB teleparallel gravity

Abstract

In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type fT,B,∇μT,∇μB , where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.