Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking

Understand

In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function $f(T,\phi)$ of the torsion scalar $T$ and a scalar field $\phi$, plus the kinetic term of this latter.

• It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations.
• In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lorentz rotation of the tetrad field.
• After integrating out all the auxiliary modes, we obtain a second order action for the scalar and tensor propagating modes and their power spectrum generated during inflation.