BF gravity with Immirzi parameter and cosmological constant

TL;DR

This paper extends a BF-type action principle for general relativity to include a cosmological constant, maintaining equivalence with the Holst action and facilitating matter coupling.

Contribution

It introduces a modified BF action that incorporates the cosmological constant while preserving the original equations of motion, advancing the framework for matter coupling in gravity theories.

Findings

The new action reproduces Einstein's equations with a cosmological constant.

It maintains equivalence with the Holst action without extra restrictions.

Facilitates future matter coupling in the CMPR framework.

Abstract

The action principle of the BF type introduced by Capovilla, Montesinos, Prieto, and Rojas (CMPR) which describes general relativity with Immirzi parameter is modified in order to allow the inclusion of the cosmological constant. The resulting action principle is on the same footing as the original Plebanski action in the sense that the equations of motion coming from the new action principle are equivalent to the Holst action principle plus a cosmological constant without the need of imposing additional restrictions on the fields. We consider this result a relevant step towards the coupling of matter fields to gravity in the framework of the CMPR action principle.