A minimal set of invariants as a systematic approach to higher order
  gravity models: Physical and Cosmological Constraints
  We compare higher order gravity models to observational constraints from
magnitude-redshift supernova data, distance to the last scattering surface of
the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed
systematic approach to higher order gravity models based on minimal sets of
curvature invariants, and select models that pass some physical acceptability
conditions (free of ghost instabilities, real and positive propagation speeds,
and free of separatrices). Models that satisfy these physical and observational
constraints are found in this analysis and do provide fits to the data that are
very close to those of the LCDM concordance model. However, we find that the
limitation of the models considered here comes from the presence of
superluminal mode propagations for the constrained parameter space of the
models.
