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In the context of modified teleparallel gravity, we study the generation ofprimordial density fluctuations in a general scalar-torsion theory whoseLagrangian 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 wellknown that generic modifications of teleparallel gravity are not invariantunder six-parameter local Lorentz transformations. In order to restore thelocal Lorentz symmetry, we have incorporated six additional degrees of freedomin the form of Goldstone modes of the symmetry breaking through a Lorentzrotation of the tetrad field. After integrating out all the auxiliary modes, weobtain a second order action for the scalar and tensor propagating modes andtheir power spectrum generated during inflation. It is found that an explicitmass term emerges in the second order action for curvature perturbation,describing the imprints of local Lorentz violation at first-order of slow-roll.We show that only inflationary models with nonminimal coupling functions$f(T,\phi)$ which are non-linear in $T$, including the case of $f(T)$ gravitywith minimally coupled scalar field, can generate primordial fluctuations. Fora concrete model of inflation, we study the power-law potential by using thelatest Planck data.

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