An axiomatic purification of gravity

Abstract

A theory of gravity is deduced from the axioms of the premetric program. The starting point is the conservation of energy and momenta, and the equivalence of gravitation and inertia. The latter is what leads to the framework of the so called purified gravity. The local and linear constitutive relation has 14 components when it is assumed to be metrical, but the compatibility of the constitutive relation with an action principle fixes uniquely the theory of Coincident General Relativity. The premetric formalism of purified gravity has a direct analogy with massive electromagnetism, the Planck mass corresponding to the Proca mass of the gauge boson. The metric emerges as a Stueckelberg field, and the graviton as a Goldstone boson of the broken symmetry.

32 pages, 2 figures, 2 tables

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Cited by in corpus (17)

• General covariant symmetric teleparallel cosmology
• Cosmological bouncing solutions in f(T,B) gravity
• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Teleparallel axions and cosmology
• Nonmetricity theories and aspects of gauge symmetry
• Pregeometric First Order Yang-Mills Theory
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Cosmic Growth in $f(T)$ Teleparallel Gravity
• Scale-invariant cosmology in de Sitter gauge theory
• Spatially covariant gravity with nonmetricity
• Generalised Proca Theories in Teleparallel Gravity
• Energy in the Relativistic Theory of Gravity
• Gauge-invariant post-Newtonian perturbations in symmetric teleparallel gravity
• The canonical energy-momentum currents in cosmology
• Lost in translation: the Abelian affine connection (in the coincident gauge)
• White Dwarf Envelops and Temperature Corrections in Exponential $f(T)$ Gravity