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

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.

6 pages, to be published

References in corpus (8)

• Modified teleparallel gravity: inflation without inflaton
• Cosmological perturbations in f(T) gravity
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Conformal transformation in $f(T)$ theories
• Remnant group of local Lorentz transformations in f(T) theories
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity
• Kaluza-Klein theory for teleparallel gravity

Cited by in corpus (5)

• Higgs inflation and teleparallel gravity
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Logamediate Inflation in f(T) Teleparallel Gravity
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Role of spacetime boundaries in Einstein's other gravity