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.

arXiv comment6 pages, to be published

References in corpus (32)

• f(R) Theories Of Gravity
• Modified Gravity and Cosmology
• f(R) theories
• Modified teleparallel gravity: inflation without inflaton
• f(T) Gravity and local Lorentz invariance
• Matter Bounce Cosmology with the f(T) Gravity
• Cosmological perturbations in f(T) gravity
• The covariant formulation of f(T) gravity
• "Teleparallel" Dark Energy
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Large-scale Structure in f(T) Gravity
• Conformal transformation in $f(T)$ theories
• Dynamics of Teleparallel Dark Energy
• Problems with Propagation and Time Evolution in f(T) Gravity
• Cosmological dynamics of tachyonic teleparallel dark energy
• Remnant group of local Lorentz transformations in f(T) theories
• Primordial Fluctuations within Teleparallelism
• Teleparallel quintessence with a nonminimal coupling to a boundary term
• Tachyonic Teleparallel Dark Energy
• General relativity as an attractor for scalar-torsion cosmology
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity
• Singularity Problem in Teleparallel Dark Energy Models
• Teleparallel Dark Energy with Purely Non-minimal Coupling to Gravity
• Notes on teleparallel cosmology with nonminimally coupled scalar field
• Acausality and Nonunique Evolution in Generalized Teleparallel Gravity
• A novel teleparallel dark energy model
• Post-Newtonian Approximation of Teleparallel Gravity Coupled with a Scalar Field
• Kaluza-Klein theory for teleparallel gravity
• Parametrized Post-Newtonian Limit of Teleparallel Dark Energy Model
• Onset of acceleration in a Universe initially filled by dark and baryonic matters in nonminimally coupled teleparallel model
• Teleparallel Gravity in Five Dimensional Theories

Cited by in corpus (14)

• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Gravitational waves in modified teleparallel theories of gravity
• Higgs inflation and teleparallel gravity
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Logamediate Inflation in f(T) Teleparallel Gravity
• Stability of scalar perturbations in scalar-torsion $f(T,\varphi )$ gravity theories in the presence of a matter fluid
• Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking
• Slow-roll inflation in generalized scalar-torsion gravity
• Role of spacetime boundaries in Einstein's other gravity
• Scalar-Tensor Teleparallel Gravity With Boundary Term by Noether Symmetries
• Perturbations of bounce inflation scenario from $f(T)$ modified gravity revisited
• Inflation and Primordial Fluctuations in $F(T)$ Gravity's Rainbow
• Observing Geometrical Torsion
• Global portraits of nonminimal teleparallel inflation