Geometrical Trinity of Unimodular Gravity

Abstract

We construct a Weyl transverse diffeomorphism invariant theory of teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to unimodular gravity (as well as Einstein's general relativity with an adjustable cosmological constant) at the non-linear level. Combined with our earlier construction of a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity, unimodular gravity is represented in three alternative ways.

16 pages

References in corpus (16)

• The teleparallel equivalent of general relativity
• Transverse Fierz-Pauli symmetry
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• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Possible consistent model of parity violations in the symmetric teleparallel gravity
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• Scalarized Black Holes in Teleparallel Gravity
• Weyl transverse gravity (WTDiff) and the cosmological constant
• Conformal Invariant Teleparallel Cosmology
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• On Gravitational Energy in Conformal Teleparallel Gravity
• Dynamical features of $f(T,B)$ cosmology

Cited by in corpus (11)

• Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions
• Gibbons-Hawking-York boundary terms and the generalized geometrical trinity of gravity
• Kantowski-Sachs spherically symmetric solutions in teleparallel $F(T)$ gravity
• Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity
• A polynomial affine model of gravity: after ten years
• Gravitational radiation from binary systems in Unimodular gravity
• Nonexistence of a parent theory for general relativity and unimodular gravity
• Scalar Field Static Spherically Symmetric Solutions in Teleparallel $F(T)$ Gravity
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor
• Electromagnetic Sources Teleparallel Robertson--Walker $F(T)$-Gravity Solutions
• Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions