Cosmological perturbations in modified teleparallel gravity models: Boundary term extension

Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are mostly not equivalent to the traditional route to modified gravity. $f(T,B)$ gravity is one such gravitational theory where the second and fourth order contributions to the field equations are decoupled. In this work, we explore the all important cosmological perturbations of this new framework of gravity. We derive the gravitational propagation equation, its vector perturbation stability conditions, and its scalar perturbations. Together with the matter perturbations, we derive the effective gravitational constant in this framework, and find an interesting branching behaviour that depends on the particular gravitational models being probed. We close with a discussion on the relation of these results with other gravitational theories.