On the Chern-Simons State in General Relativity and Modified Gravity Theories

The Chern-Simons state is one solution to quantum constraints of gravity in the context of general relativity (CR) theory if we use Ashtekar's variables and if one orders the constraints with the triads to the left. Six years ago Krasnov introduced a certain class of modified gravity theories by replacing the cosmological constant by a "cosmological function of the curvature". If this function is a constant we come back to GR. In this note we review how the Chern-Simons state is one solution to the constraints of CR and we state the problem to face if we wish a generalized Chern-Simons state for the modified Krasnov's theories.