Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?

TL;DR

This paper explores whether torsion in teleparallel gravity can generate primordial fluctuations without local Lorentz symmetry, concluding it cannot produce sufficient density inhomogeneity for inflation.

Contribution

It demonstrates that in extended teleparallel inflation models, torsion alone cannot generate the necessary primordial fluctuations due to Lorentz symmetry violation effects.

Findings

Scalar perturbations cannot survive to horizon crossing in these models.

Torsion-based inflation cannot produce enough primordial density fluctuations.

Local Lorentz violation impacts the generation of primordial fluctuations.

Abstract

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 $T$ that effectively includes $f(T)$ 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.