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

TL;DR

This paper examines the Plebanski formulation of general relativity with a cosmological constant and Immirzi parameter, revealing modifications to the Lagrange multiplier and implications for modified gravity theories.

Contribution

It demonstrates that the Lagrange multiplier gains a trace component in this setting, affecting the structure of the field equations and related theories.

Findings

Lagrange multiplier acquires a trace part with both cosmological constant and Immirzi parameter

Implications for the structure of modified gravity theories

Insights into the geometric interpretation of the Plebanski action

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.