Pseudoinvariance and the extra degree of freedom in f(T) gravity

Abstract

Nonlinear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudoinvariant under local Lorentz transformations of the tetrad field. This procedure consequently leads to the loss of the local pseudoinvariance and the appearance of additional degrees of freedom (d.o.f.). The constraint structure of f(T) gravity suggests the existence of one extra d.o.f. when compared with GR, which should describe some aspect of the orientation of the tetrad. The purpose of this article is to better understand the nature of this extra d.o.f. by means of a toy model that mimics essential features of f(T) gravity. We find that the nonlinear modification of a Lagrangian L possessing a local rotational pseudoinvariance produces two types of solutions. In one case the original gauge-invariant variables -- the analogue of the metric in teleparallelism -- evolve like when governed by the (nondeformed) Lagrangian L; these solutions are characterized by a (selectable) constant value of its Lagrangian, which is the manifestation of the extra d.o.f. In the other case, the solutions do contain new dynamics for the original gauge-invariant variables, but the extra d.o.f. does not materialize because the Lagrangian remains invariant on-shell. Coming back to f(T) gravity, the first case includes solutions where the torsion scalar T is a constant, to be chosen at the initial conditions (extra d.o.f.), and no new dynamics for the metric is expected. The latter case covers those solutions displaying a genuine modified gravity; T is not a constant, but it is (on-shell) invariant under Lorentz transformations depending only on time. Both kinds of f(T) solutions are exemplified in a flat FLRW universe. Finally, we present a toy model for a higher-order Lagrangian with rotational invariance [analogous to f(R) gravity] and derive its constraint structure and number of d.o.f.

22 pages, 2 tables, no figures, comments welcome; matches the published version

References in corpus (16)

• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Cosmological perturbations in f(T) gravity
• Degrees of freedom of $f(T)$ gravity
• Conformal transformation in $f(T)$ theories
• Remnant group of local Lorentz transformations in f(T) theories
• Hamiltonian formulation of teleparallel gravity
• Kerr geometry in f(T) gravity
• Non-Linear Obstructions for Consistent New General Relativity
• Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity
• Reflections on the covariance of modified teleparallel theories of gravity
• McVittie solution in f(T) gravity
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• Role of spacetime boundaries in Einstein's other gravity
• A Solution to Symmetric Teleparallel Gravity
• Disformal transformations in modified teleparallel gravity

Cited by in corpus (24)

• Teleparallel Gravity: From Theory to Cosmology
• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• Modified gravity: a unified approach
• Foundational issues in f(T) gravity theory
• Review of the Hamiltonian analysis in teleparallel gravity
• Minkowski space in $f(T)$ gravity
• Non-trivial Minkowski backgrounds in f(T) gravity
• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• General cosmological perturbations in teleparallel gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• BTZ gems inside regular Born-Infeld black holes
• General Teleparallel Modifications of Schwarzschild Geometry
• A geometric view on local Lorentz transformations in teleparallel gravity
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• The Gauss-Bonnet topological scalar in the Geometric Trinity of Gravity
• Matching tetrads in f(T) gravity
• Teleparallel bigravity
• $f(T)$ Gravity: Background Dependence and Propagating Degrees of Freedom
• Reconstructing modified and alternative theories of gravity
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Global portraits of nonminimal teleparallel inflation