Eur. Phys. J. C (2018) 78: 568
https://doi.org/10.1140/epjc/s10052-018-6050-3

Regular Article - Theoretical Physics

Counting components in the Lagrange multiplier formulation of teleparallel theories

¹ Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou, 225009, China
² School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
³ Department of Physics, National Central University, Chungli, 32001, Taiwan, ROC
⁴ Graduate Institute of Astronomy, National Central University, Chungli, 32001, Taiwan, ROC
⁵ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan, ROC

^* e-mail: ongyenchin@gmail.com

Received: 15 April 2018
Accepted: 4 July 2018
Published online: 10 July 2018

Abstract

We investigate the Lagrange multiplier formulation of teleparallel theories, including f(T) gravity, in which the connection is not set to zero a priori and compare it with the pure frame theory. We show explicitly that the two formulations are equivalent, in the sense that the dynamical equations have the same content. One consequence is that the manifestly local Lorentz invariant f(T) theory cannot be expected to be free of pathologies, which were previously found to plague f(T) gravity formulated in the usual pure frame approach.