Title: Generating Primordial Fluctuations from Modified Teleparallel Gravity: Single-Field and Multifield Inflation Scenarios

Abstract: In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. To restore local Lorentz symmetry, we incorporate six additional degrees of freedom as Goldstone modes of the symmetry breaking through a Lorentz rotation of the tetrad field. After integrating out all auxiliary modes, we obtain a second-order action for the scalar and tensor propagating modes, and their power spectrum generated during inflation. An explicit mass term emerges in the second-order action for curvature perturbation, describing the imprints of local Lorentz violation at the first-order of slow-roll. Both cases, single-field inflation and multifield inflation, are considered in this analysis, allowing us to explore the distinct impacts of local Lorentz symmetry breaking on the dynamics and observational signatures of primordial fluctuations in different inflationary scenarios.