A note on the Plebanski action with cosmological constant and an Immirzi parameter

Abstract

We study the field equations of the Plebanski action for general relativity when both the cosmological constant and an Immirzi parameter are present. We show that the Lagrange multiplier, which usually gets identified with the Weyl curvature, now acquires a trace part. Some consequences of this for a class of modified gravity theories recently proposed in the literature are briefly discussed.

14 pages. v2: factor 2 corrected, updated references

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Cited by in corpus (15)

• Gravity and Unification: A review
• $BF$ gravity
• Bi-metric theory of gravity from the non-chiral Plebanski action
• On the Relations between Gravity and BF Theories
• Unification of gravity, gauge fields, and Higgs bosons
• Debye entropic force and modified Newtonian dynamics
• Pauli-Fierz mass term in modified Plebanski gravity
• BF gravity with Immirzi parameter and cosmological constant
• Spin connection formulations of real Lorentzian General Relativity
• BF gravity with Immirzi parameter and matter fields
• Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter
• Anti-self-dual gravity and supergravity from a pure connection formulation
• Canonical structure of minimal varying $\Lambda$ theories
• Polysymplectic formulation for BF gravity with Immirzi parameter
• Minimally modified self-dual 2-forms gravity