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Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?
Arbitrary generalization to the teleparallel equivalent of general relativity
loses local Lorentz invariance to reparametrize the orthonormal coordinate
system and gives rise to asymmetry field equations. We investigate consequences
of local Lorentz violation to primordial fluctuations in extended single field
inflationary models based on the scalar-tensor formulation of the torsion
scalar that effectively includes gravity as a special case. We show
that despite some asymmetry part of the field equations are removed in a
spatially homogeneous and isotropic cosmic background, no subhorizon
scalar-perturbation mode can survive by the time of horizon crossing. As a
result, any scalar field mediated in torsion cannot generate enough primordial
density inhomogeneity alone, even if it brings some de Sitter background
solutions in generalized teleparallel gravity.Comment: 6 pages, to be publishe
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