Trace-free Einstein gravity as a constrained bigravity theory

Abstract

Trace-free Einstein gravity is a prominent alternative to general relativity, which has two versions: one in which the energy-momentum conservation is assumed a priori and another in which it is not. In the first version, the cosmological constant arises as an integration constant. We report two diffeomorphism-invariant actions for trace-free Einstein gravity in which the energy-momentum conservation emerges directly from the equations of motion. The first action is based on the metric, while the second action is based on the tetrad and connection where the conservation of the energy-momentum holds if torsion vanishes. To achieve this, auxiliary fields but otherwise dynamical are introduced in the corresponding actions, which have the form a constrained bigravity theory. These results constitute a significant advance in our understanding of trace-free Einstein gravity.

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Cited by in corpus (6)

• Cosmological constant as an integration constant
• From spacetime thermodynamics to Weyl transverse gravity
• Exploring thermodynamics inconsistencies in unimodular gravity: a comparative study of two energy diffusion functions
• Trace-free Einstein gravity as two interacting constrained $BF$ theories
• Classical and quantum trace-free Einstein cosmology
• Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor