Conformal/Poincaré Coset, cosmology, and descendants of Lovelock terms

We calculate six invariant terms of a gravitational field theory that nonlinearly realizes the conformal/Poincar\'e quotient and reduce to the known conformal Galileons in the limit when only the conformal mode is kept. Five of the six terms are regular coset terms, while the sixth is a Wess-Zumino (WZ) term that gives the well-known gravitational action for the trace anomaly. The obtained terms can be embedded in a quantum effective field theory (EFT) without spoiling their key features, although at a cost of certain fine-tunings. The additional massive modes that appear in the EFT would have been troublesome, however, for sub-Planckian curvatures their masses are (super)-Planckian, and therefore the respective states are outside of the EFT regime. We discuss certain novel cosmological solution of this theory and their validity within the EFT. Furthermore, we show that the obtained 4D terms, except the WZ term, can also be derived from higher dimensional Lovelock terms by reducing the latter to the genuinely four-dimensional terms according to a well-defined algorithm.