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BRST symmetry for Regge-Teitelboim based minisuperspace models

The Einstein-Hilbert action in the context of Higher derivative theories is considered for finding out their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et. al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge fixing conditions. Further, the BRST (conserved) charge is computed which plays an important role in defining the physical states from the total Hilbert space of states. The finite field dependent BRST (FFBRST) formulation is also studied in this context where the Jacobian for functional measure is illustrated specifically.