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.Comment: 14 pages. v2: factor 2 corrected, updated reference