Generating primordial fluctuations from modified teleparallel gravity with local Lorentz-symmetry breaking

Abstract

In the context of modified teleparallel gravity, we study the generation of primordial density fluctuations in a general scalar-torsion theory whose Lagrangian density is an arbitrary function $f(T,\varphi )$ of the torsion scalar $T$ and a scalar field $\varphi$, plus the kinetic term of this latter. It is well known that generic modifications of teleparallel gravity are not invariant under six-parameter local Lorentz transformations. In order to restore the local Lorentz symmetry, we have incorporated six additional degrees of freedom in the form of Goldstone modes of the symmetry breaking through a Lorentz rotation of the tetrad field. After integrating out all the auxiliary modes, we obtain a second order action for the scalar and tensor propagating modes and their power spectrum generated during inflation. It is found that an explicit mass term emerges in the second order action for curvature perturbation, describing the imprints of local Lorentz violation at first-order of slow-roll. We show that only inflationary models with nonminimal coupling functions $f(T,\varphi )$ which are non-linear in $T$, including the case of $f(T)$ gravity with minimally coupled scalar field, can generate primordial fluctuations. For a concrete model of inflation, we study the power-law potential by using the latest Planck data.

10 pages, 2 figures, Accepted for publication in PLB

References in corpus (12)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Spontaneous Lorentz and Diffeomorphism Violation, Massive Modes, and Gravity
• Inflation and String Theory
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Dynamical features of scalar-torsion theories
• TASI Lectures on Inflation
• Gauge Structure of Teleparallel Gravity
• Gravity Theories with Background Fields and Spacetime Symmetry Breaking
• Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?